user8157: Recently, Bhikkhu Sujato wrote:

It is no coincidence that these elaborate texts are often addressed to
the brahmins, who were the self-proclaimed spiritual leaders of the
time. The brahmins were the custodians of the most sophisticated texts
in ancient India up to this time, the Vedic literature. It seems that
one aim of the Dīgha was to impress such learned men.
The Long Discourses: Dhamma as literature and compilation

There also this introduction on Access to Insight (which cites Bhikkhu Bodhi and Joy Manné):

The "Long" Discourses (Pali digha = "long") consists of 34 suttas,
including the longest ones in the Canon. The subject matter of these
suttas ranges widely, from colorful folkloric accounts of the beings
inhabiting the deva worlds (DN 20) to down-to-earth practical
meditation instructions (DN 22), and everything in between. Recent
scholarship suggests that a distinguishing trait of the Digha Nikaya
may be that it was "intended for the purpose of propaganda, to attract
converts to the new religion."1

Bhikkhu Bodhi, Connected Discourses of the Buddha (Somerville, Mass.: Wisdom Publications, 2000), p.31, referring to Joy Manné's
"Categories of Sutta in the Pali Nikayas and Their Implications for
Our Appreciation of the Buddhist Teaching and Literature," Journal of
the Pali Text Society 15 (1990): 29-87.

Sutta Pitaka
The Basket of Suttas

Is there evidence (such as contradictions with other suttas) suggesting the Buddha did not speak the Digha Nikaya?
In there any evidence in the suttas where the Buddha said he would teach a different modified Dhamma ("propaganda") merely for the purpose of converting Brahmins & other outsiders?
Is there any evidence in the suttas showing the Buddha was "flexible" in his teaching of Dhamma? Or do the suttas show the Buddha wished his teachings to remain consistent & clearly representative of what he taught?

user14866: 
Is there any evidence in the suttas showing the Buddha was "flexible" in his teaching of Dhamma?

He was not a little flexible when one spoke A-dhamma but did not limit the Tataghata to his speech at the same time, as the only that should be taken as that of the Tataghata.
Once the Budddha rebuked some who told that another does teach something the Buddha did not say by "What ever Dhamma a Noble one speaks, it is the Dhamma of the Tatagatha". One may google it ... or ask a monk for details if able to leave house. It was, btw, on the teaching one gave, that one should seriously reflect one's own attainments and that of others, periodical!
[off (ordinary) cause: this is not given for trade, stacks, exchange or Buddh-ism and other binding purposes for the world but dedicated for refuge toward liberation]

user254: Is there any evidence in the suttas showing the Buddha was "flexible" in his teaching of Dhamma? Or do the suttas show the Buddha wished his teachings to remain consistent & clearly representative of what he taught?
I think the Buddha explained Dhamma, and that the explanation was adapted according to who he was addressing.
This footnote to the Sigalovada sutta, for example, suggests that "worshipping the six directions" was a Vedic ritual, and the Buddha takes advantage of the occasion to teach a different doctrine.
But that's not to say that the doctrine is incompatible with the doctrine taught in other suttas (but it is rather different to the Rhinoceros sutta for example).
Or according to Piya Tan the Aggañña Sutta (DN 27) is addressed to Brahmins (i.e. probationary monks who were Brahmins) and is perhaps a parody of Brahminical creation myths. The subject matter is "fantastic" but the doctrine (i.e. that the fall is due to craving "nourishment") is again not incompatible with other suttas.
I don't mean to generalise about the whole Digha Nikaya. But you ask whether he was "flexible, or, wished to remain consistent" -- perhaps he was flexible 'and' remained consistent.
I think that's famously part of his ability as Buddha, i.e. to know how to teach different people.
One of the suttas which shows that "the Buddha wished his teachings to remain consistent & clearly representative of what he taught" is (perhaps ironically, given the question) the Maha-parinibbana Sutta i.e. DN 16 -- which includes the "four great references" and so on.

Incidentally in this answer Bonn says ...

I can answer the question if I still quote the original text from Tipitaka and Atthakatha without making them conflict with each other.
I never try to make Tipitaka conflict with each other, never make Atthakathā conflict with each other, and never cut any part of Tipitaka and Atthakathā off.

... and in this answer ...

People who can understand the noble truth from tipitaka must can deconflict every uncleared word of tipitaka

... so I presume it's possible that, I think it's the opinion of e.g. Thai/Buddhist scholars that, the teachings are consistent.
In my opinion though (I don't know about Bonn's) to say "they're consistent" might need some flexibility (and good-will, and if not 'faith' exactly then at least a willingness to listen) in how you interpret them -- words have a range of meanings, they're often used metaphorically, part of the doctrine is not being over-attached to specific views, I think they are adapted/suited to the specific audience (often a reply to a specific question), etc.
Perhaps my opinion (above) is overly rosy though, and there are bits (of suttas) -- not all in the Digha Nikaya -- which I overlook or ignore. I don't think I'd want to argue the doctrinal details you identify in your answer -- some of your comments (e.g. about namarupa) I just don't understand or have no opinion about; and some (e.g. about DN 27) isn't how I read that sutta (and I'm content with my reading of it but I'm not sure it would benefit anyone to try to argue about it with you).

user14842: Is there evidence (such as contradictions with other suttas)
suggesting the Buddha did not speak the Digha Nikaya?

The four primary Theravadin Nikayas, namely Digha Nikaya, Majjhima Nikaya, Samyutta Nikaya, and Anguttara Nikaya contained no contradiction with each other.
You may also wish to scrutinize the Buddhist Councils "convention" and their outcomes to ascertain the level of "authenticity"/preservation of the Buddha's teachings.
In there any evidence in the suttas where the Buddha said he would 
teach a different modified Dhamma ("propaganda") merely for the 
purpose of converting Brahmins & other outsiders?

In the suttas, the Buddha pretty much taught the same thing to everyone. There was no "special" teachings for select groups of disciples or audiences.
Is there any evidence in the suttas showing the Buddha was "flexible"
in his teaching of Dhamma? Or do the suttas show the Buddha wished 
his teachings to remain consistent & clearly representative of what 
he taught?

The Buddha had over 40 years to teach. So, he did teach the same thing in many ways depending on the intellectual level of his listeners. And he had 40 years to admonish/correct disciples who developed wrong views of his teachings.

user471: It was the Buddha who spoke the words of the DN, but it was compiled, collated, arranged and rearranged by the Sangha centuries after his passing. The DN was not fabricated. Also the Buddha certainly never said, "Today I'm going to speak Digha Nikaya 1".
The Sangha may have rearranged the suttas into the sequence of the DN today with intention to define the difference between the Buddha's teachings and other religions (in DN 1), the role of the monks (in DN 2), the role of the lay followers (in DN 31), the continuation of Buddhism after the Buddha passes away (in DN 16) etc. There might have been some specific intention behind this arrangement, perhaps to create a constitution of sorts.

OP: Is there evidence (such as contradictions with other suttas) suggesting the Buddha did not speak the Digha Nikaya?

There is no evidence of contradiction between the nikayas.

OP: In there any evidence in the suttas where the Buddha said he would teach a different modified Dhamma ("propaganda") merely for the
  purpose of converting Brahmins & other outsiders?

No. The Buddha taught the same thing to monks, lay followers and outsiders, according to SN 42.7:

“To me, the monks and nuns are like the good field. I teach them the
  Dhamma that’s good in the beginning, good in the middle, and good in
  the end, meaningful and well-phrased. And I reveal a spiritual
  practice that’s entirely full and pure. Why is that? Because they live
  with me as their island, protection, shelter, and refuge.
To me, the 
  laymen and laywomen are like the average field. I also teach them the
  Dhamma that’s good in the beginning, good in the middle, and good in
  the end, meaningful and well-phrased. And I reveal a spiritual
  practice that’s entirely full and pure. Why is that? Because they live
  with me as their island, protection, shelter, and refuge.
To me, the 
  ascetics, brahmins, and wanderers who follow other paths are like the
  poor field, the bad ground of sand and salt. I also teach them the
  Dhamma that’s good in the beginning, good in the middle, and good in
  the end, meaningful and well-phrased. And I reveal a spiritual
  practice that’s entirely full and pure. Why is that? Hopefully they
  might understand even a single sentence, which would be for their
  lasting welfare and happiness.

So, he did not teach followers and non-followers differently..

OP: Is there any evidence in the suttas showing the Buddha was "flexible" in his teaching of Dhamma? Or do the suttas show the Buddha
  wished his teachings to remain consistent & clearly representative of
  what he taught?

WHAT he taught was the same, but HOW he taught it, could be different according to the Kesi Sutta (AN 4.111):

"Kesi, I train a tamable person [sometimes] with gentleness,
  [sometimes] with harshness, [sometimes] with both gentleness &
  harshness.
"In using gentleness, [I teach:] 'Such is good bodily conduct. Such is
  the result of good bodily conduct. Such is good verbal conduct. Such
  is the result of good verbal conduct. Such is good mental conduct.
  Such is the result of good mental conduct. Such are the devas. Such
  are human beings.'
"In using harshness, [I teach:] 'Such is bodily misconduct. Such is
  the result of bodily misconduct. Such is verbal misconduct. Such is
  the result of verbal misconduct. Such is mental misconduct. Such is
  the result of mental misconduct. Such is hell. Such is the animal
  womb. Such the realm of the hungry shades.'
"In using gentleness & harshness, [I teach:] 'Such is good bodily
  conduct. Such is the result of good bodily conduct. Such is bodily
  misconduct. Such is the result of bodily misconduct. Such is good
  verbal conduct. Such is the result of good verbal conduct. Such is
  verbal misconduct. Such is the result of verbal misconduct. Such is
  good mental conduct. Such is the result of good mental conduct. Such
  is mental misconduct. Such is the result of mental misconduct. Such
  are the devas. Such are human beings. Such is hell. Such is the animal
  womb. Such the realm of the hungry shades.'"
"And if a tamable person doesn't submit either to a mild training or
  to a harsh training or to a mild & harsh training, what do you do?"
"If a tamable person doesn't submit either to a mild training or to a
  harsh training or to a mild & harsh training, then I kill him, Kesi."
"But it's not proper for our Blessed One to take life! And yet the
  Blessed One just said, 'I kill him, Kesi.'"
"It is true, Kesi, that it's not proper for a Tathagata to take life.
  But if a tamable person doesn't submit either to a mild training or to
  a harsh training or to a mild & harsh training, then the Tathagata
  doesn't regard him as being worth speaking to or admonishing. His
  knowledgeable fellows in the holy life don't regard him as being worth
  speaking to or admonishing. This is what it means to be totally
  destroyed in the Doctrine & Discipline, when the Tathagata doesn't
  regard one as being worth speaking to or admonishing, and one's
  knowledgeable fellows in the holy life don't regard one as being worth
  speaking to or admonishing."


8157: <p>Recently, Bhikkhu Sujato wrote:</p>
<blockquote>
<p>It is no coincidence that these elaborate texts are often addressed to
the brahmins, who were the self-proclaimed spiritual leaders of the
time. The brahmins were the custodians of the most sophisticated texts
in ancient India up to this time, the Vedic literature. It seems that
one aim of the Dīgha was to impress such learned men.</p>
<p><a href="https://discourse.suttacentral.net/t/the-long-discourses-dhamma-as-literature-and-compilation/11523" rel="nofollow noreferrer">The Long Discourses: Dhamma as literature and compilation</a></p>
</blockquote>
<p>There also this introduction on <em>Access to Insight</em> (which cites Bhikkhu Bodhi and Joy Manné):</p>
<blockquote>
<p>The &quot;Long&quot; Discourses (Pali digha = &quot;long&quot;) consists of 34 suttas,
including the longest ones in the Canon. The subject matter of these
suttas ranges widely, from colorful folkloric accounts of the beings
inhabiting the deva worlds (DN 20) to down-to-earth practical
meditation instructions (DN 22), and everything in between. Recent
scholarship suggests that a distinguishing trait of the Digha Nikaya
may be that it was &quot;intended for the purpose of propaganda, to attract
converts to the new religion.&quot;1</p>
<ol>
<li>Bhikkhu Bodhi, Connected Discourses of the Buddha (Somerville, Mass.: Wisdom Publications, 2000), p.31, referring to Joy Manné's
&quot;Categories of Sutta in the Pali Nikayas and Their Implications for
Our Appreciation of the Buddhist Teaching and Literature,&quot; Journal of
the Pali Text Society 15 (1990): 29-87.</li>
</ol>
<p><a href="https://www.accesstoinsight.org/tipitaka/sutta.html#fn-1" rel="nofollow noreferrer">Sutta Pitaka
The Basket of Suttas</a></p>
</blockquote>
<p>Is there evidence (such as contradictions with other suttas) suggesting the Buddha did not speak the Digha Nikaya?</p>
<p>In there any evidence in the suttas where the Buddha said he would teach a different modified Dhamma (&quot;propaganda&quot;) merely for the purpose of converting Brahmins &amp; other outsiders?</p>
<p>Is there any evidence in the suttas showing the Buddha was &quot;flexible&quot; in his teaching of Dhamma? Or do the suttas show the Buddha wished his teachings to remain consistent &amp; clearly representative of what he taught?</p>
 14866: <blockquote>
  <p>Is there any evidence in the suttas showing the Buddha was "flexible" in his teaching of Dhamma?</p>
</blockquote>

<p>He was not a little flexible when one spoke A-dhamma but did not limit the Tataghata to his speech at the same time, as the only that should be taken as that of the Tataghata.</p>

<p>Once the Budddha rebuked some who told that another does teach something the Buddha did not say by "What ever Dhamma a Noble one speaks, it is the Dhamma of the Tatagatha". One may google it ... or ask a monk for details if able to leave house. It was, btw, on the teaching one gave, that one should seriously reflect one's own attainments and that of others, periodical!</p>

<p><em>[off (ordinary) cause: this is not given for trade, stacks, exchange or Buddh-ism and other binding purposes for the world but dedicated for refuge toward liberation]</em></p>
 254: <p><strong>Is there any evidence in the suttas showing the Buddha was &quot;flexible&quot; in his teaching of Dhamma? Or do the suttas show the Buddha wished his teachings to remain consistent &amp; clearly representative of what he taught?</strong></p>
<p>I think the Buddha explained Dhamma, and that the explanation was adapted according to who he was addressing.</p>
<p><a href="https://www.accesstoinsight.org/tipitaka/dn/dn.31.0.ksw0.html#fn-3" rel="nofollow noreferrer">This footnote</a> to the Sigalovada sutta, for example, suggests that &quot;worshipping the six directions&quot; was a Vedic ritual, and the Buddha takes advantage of the occasion to teach a different doctrine.</p>
<p>But that's not to say that the doctrine is incompatible with the doctrine taught in other suttas (but it is rather different to the Rhinoceros sutta for example).</p>
<p>Or <a href="http://www.themindingcentre.org/dharmafarer/wp-content/uploads/2009/12/2.19-Agganna-S-d27-piya.pdf" rel="nofollow noreferrer">according to Piya Tan</a> the Aggañña Sutta (DN 27) is addressed to Brahmins (i.e. probationary monks who were Brahmins) and is perhaps a parody of Brahminical creation myths. The subject matter is &quot;fantastic&quot; but the doctrine (i.e. that the fall is due to craving &quot;nourishment&quot;) is again not incompatible with other suttas.</p>
<p>I don't mean to generalise about the whole Digha Nikaya. But you ask whether he was &quot;flexible, or, wished to remain consistent&quot; -- perhaps he was flexible 'and' remained consistent.</p>
<p>I think that's famously part of his ability as Buddha, i.e. to know how to teach different people.</p>
<p>One of the suttas which shows that &quot;the Buddha wished his teachings to remain consistent &amp; clearly representative of what he taught&quot; is (perhaps ironically, given the question) the Maha-parinibbana Sutta i.e. DN 16 -- which includes the &quot;four great references&quot; and so on.</p>
<hr />
<p>Incidentally <a href="https://buddhism.stackexchange.com/a/31097/254">in this answer</a> Bonn says ...</p>
<blockquote>
<p>I can answer the question if I still quote the original text from Tipitaka and Atthakatha without making them conflict with each other.</p>
<p>I never try to make Tipitaka conflict with each other, never make Atthakathā conflict with each other, and never cut any part of Tipitaka and Atthakathā off.</p>
</blockquote>
<p>... and <a href="https://buddhism.stackexchange.com/a/29469/254">in this answer</a> ...</p>
<blockquote>
<p>People who can understand the noble truth from tipitaka must can deconflict every uncleared word of tipitaka</p>
</blockquote>
<p>... so I presume it's possible that, I think it's the opinion of e.g. Thai/Buddhist scholars that, the teachings are consistent.</p>
<p>In my opinion though (I don't know about Bonn's) to say &quot;they're consistent&quot; might need some flexibility (and good-will, and if not 'faith' exactly then at least a willingness to listen) in how you interpret them -- words have a range of meanings, they're often used metaphorically, part of the doctrine is not being over-attached to specific views, I think they are adapted/suited to the specific audience (often a reply to a specific question), etc.</p>
<p>Perhaps my opinion (above) is overly rosy though, and there are bits (of suttas) -- not all in the Digha Nikaya -- which I overlook or ignore. I don't think I'd want to argue the doctrinal details you identify <a href="https://buddhism.stackexchange.com/a/31134/254">in your answer</a> -- some of your comments (e.g. about namarupa) I just don't understand or have no opinion about; and some (e.g. about DN 27) isn't how I read that sutta (and I'm content with my reading of it but I'm not sure it would benefit anyone to try to argue about it with you).</p>
 14842: <pre><code>Is there evidence (such as contradictions with other suttas)
suggesting the Buddha did not speak the Digha Nikaya?
</code></pre>

<p>The four primary Theravadin Nikayas, namely Digha Nikaya, Majjhima Nikaya, Samyutta Nikaya, and Anguttara Nikaya contained no contradiction with each other.</p>

<p>You may also wish to scrutinize the <a href="https://en.wikipedia.org/wiki/Buddhist_councils" rel="nofollow noreferrer">Buddhist Councils</a> "convention" and their outcomes to ascertain the level of "authenticity"/preservation of the Buddha's teachings.</p>

<pre><code>In there any evidence in the suttas where the Buddha said he would 
teach a different modified Dhamma ("propaganda") merely for the 
purpose of converting Brahmins &amp; other outsiders?
</code></pre>

<p>In the suttas, the Buddha pretty much taught the same thing to everyone. There was no "special" teachings for select groups of disciples or audiences.</p>

<pre><code>Is there any evidence in the suttas showing the Buddha was "flexible"
in his teaching of Dhamma? Or do the suttas show the Buddha wished 
his teachings to remain consistent &amp; clearly representative of what 
he taught?
</code></pre>

<p>The Buddha had over 40 years to teach. So, he did teach the same thing in many ways depending on the intellectual level of his listeners. And he had 40 years to admonish/correct disciples who developed wrong views of his teachings.</p>
 471: <p>It was the Buddha who spoke the words of the DN, but it was compiled, collated, arranged and rearranged by the Sangha centuries after his passing. The DN was not fabricated. Also the Buddha certainly never said, "<em>Today I'm going to speak Digha Nikaya 1</em>".</p>

<p>The Sangha may have rearranged the suttas into the sequence of the DN today with intention to define the difference between the Buddha's teachings and other religions (in DN 1), the role of the monks (in DN 2), the role of the lay followers (in DN 31), the continuation of Buddhism after the Buddha passes away (in DN 16) etc. There might have been some specific intention behind this arrangement, perhaps to create a constitution of sorts.</p>

<blockquote>
  <p><strong>OP:</strong> Is there evidence (such as contradictions with other suttas) suggesting the Buddha did not speak the Digha Nikaya?</p>
</blockquote>

<p>There is no evidence of contradiction between the nikayas.</p>

<blockquote>
  <p><strong>OP:</strong> In there any evidence in the suttas where the Buddha said he would teach a different modified Dhamma ("propaganda") merely for the
  purpose of converting Brahmins &amp; other outsiders?</p>
</blockquote>

<p>No. The Buddha taught the same thing to monks, lay followers and outsiders, according to <a href="https://suttacentral.net/sn42.7/en/sujato" rel="nofollow noreferrer">SN 42.7</a>:</p>

<blockquote>
  <p>“To me, the monks and nuns are like the good field. I teach them the
  Dhamma that’s good in the beginning, good in the middle, and good in
  the end, meaningful and well-phrased. And I reveal a spiritual
  practice that’s entirely full and pure. Why is that? Because they live
  with me as their island, protection, shelter, and refuge.</p>
  
  <p>To me, the 
  laymen and laywomen are like the average field. I also teach them the
  Dhamma that’s good in the beginning, good in the middle, and good in
  the end, meaningful and well-phrased. And I reveal a spiritual
  practice that’s entirely full and pure. Why is that? Because they live
  with me as their island, protection, shelter, and refuge.</p>
  
  <p>To me, the 
  ascetics, brahmins, and wanderers who follow other paths are like the
  poor field, the bad ground of sand and salt. I also teach them the
  Dhamma that’s good in the beginning, good in the middle, and good in
  the end, meaningful and well-phrased. And I reveal a spiritual
  practice that’s entirely full and pure. Why is that? Hopefully they
  might understand even a single sentence, which would be for their
  lasting welfare and happiness.</p>
</blockquote>

<p>So, he did not teach followers and non-followers differently..</p>

<blockquote>
  <p><strong>OP:</strong> Is there any evidence in the suttas showing the Buddha was "flexible" in his teaching of Dhamma? Or do the suttas show the Buddha
  wished his teachings to remain consistent &amp; clearly representative of
  what he taught?</p>
</blockquote>

<p>WHAT he taught was the same, but HOW he taught it, could be different according to the <a href="https://www.accesstoinsight.org/tipitaka/an/an04/an04.111.than.html" rel="nofollow noreferrer">Kesi Sutta (AN 4.111)</a>:</p>

<blockquote>
  <p>"Kesi, I train a tamable person [sometimes] with gentleness,
  [sometimes] with harshness, [sometimes] with both gentleness &amp;
  harshness.</p>
  
  <p>"In using gentleness, [I teach:] 'Such is good bodily conduct. Such is
  the result of good bodily conduct. Such is good verbal conduct. Such
  is the result of good verbal conduct. Such is good mental conduct.
  Such is the result of good mental conduct. Such are the devas. Such
  are human beings.'</p>
  
  <p>"In using harshness, [I teach:] 'Such is bodily misconduct. Such is
  the result of bodily misconduct. Such is verbal misconduct. Such is
  the result of verbal misconduct. Such is mental misconduct. Such is
  the result of mental misconduct. Such is hell. Such is the animal
  womb. Such the realm of the hungry shades.'</p>
  
  <p>"In using gentleness &amp; harshness, [I teach:] 'Such is good bodily
  conduct. Such is the result of good bodily conduct. Such is bodily
  misconduct. Such is the result of bodily misconduct. Such is good
  verbal conduct. Such is the result of good verbal conduct. Such is
  verbal misconduct. Such is the result of verbal misconduct. Such is
  good mental conduct. Such is the result of good mental conduct. Such
  is mental misconduct. Such is the result of mental misconduct. Such
  are the devas. Such are human beings. Such is hell. Such is the animal
  womb. Such the realm of the hungry shades.'"</p>
  
  <p>"And if a tamable person doesn't submit either to a mild training or
  to a harsh training or to a mild &amp; harsh training, what do you do?"</p>
  
  <p>"If a tamable person doesn't submit either to a mild training or to a
  harsh training or to a mild &amp; harsh training, then I kill him, Kesi."</p>
  
  <p>"But it's not proper for our Blessed One to take life! And yet the
  Blessed One just said, 'I kill him, Kesi.'"</p>
  
  <p>"It is true, Kesi, that it's not proper for a Tathagata to take life.
  But if a tamable person doesn't submit either to a mild training or to
  a harsh training or to a mild &amp; harsh training, then the Tathagata
  doesn't regard him as being worth speaking to or admonishing. His
  knowledgeable fellows in the holy life don't regard him as being worth
  speaking to or admonishing. This is what it means to be totally
  destroyed in the Doctrine &amp; Discipline, when the Tathagata doesn't
  regard one as being worth speaking to or admonishing, and one's
  knowledgeable fellows in the holy life don't regard one as being worth
  speaking to or admonishing."</p>
</blockquote>
