Q:

What is the reason for the blue color of an ammoniated electron?

I am quoting a line from a book regarding reactivity of alkali metals with liquid ammonia.

The blue colour of the solution is due to the ammoniated electron which absorbs energy in the visible region of light and thus imparts blue colour to the solution

Now my question is:

How does the independent electron get excited (without transitional levels)?

Why do salts of particular alkaline metal always have a fixed flame color if transitions of electrons can be from any energy level.
(I am asking this question based on my knowledge of school where we only studied transitions among hydrogen like species)

A:

Both of your questions could benefit from more background, so please forgive me if I understood something wrong. However, I'll try to answer as best I can:

The excess electron in liquid ammonia is not really independent, otherwise, as you stated correctly, the electron would not absorb a certain wavelength but act as a black radiator/absorber like in a plasma (for example the sun). However, how the electron is bound and how the transitional states are formed is not completely understood yet. In this paper, I found the following sentence: "The excess electron in liquid ammonia ("ammoniated electron") is commonly viewed as a cavity electron in which the s-type wave function fills the interstitial void between 6 and 9 ammonia molecules." And then they go on to present a different hypothesis...
In a flame, the spectrum is recorded in the gas phase and formed not by the salt but by the individual atoms (even if you put the salt into the flame). Thus the spectrum depends only on the elements contained in the salt, not on the type of salt. This is different, if the spectroscopy is performed in the liquid phase of alkali metal halides. There the spectrum depends on the mole ratio of the anions and cations.

A:

To expand on Thawn's answer to #1 a bit:
In quantum systems, a particle is bound to discrete states when it is constrained by a sufficiently deep potential well; otherwise its energy is continuous$^\dagger$.  So, the existence of solvated electrons (alt., electrides) implies that the potential field established in certain solvents in certain situations contains "deep enough" potential wells to bind an electron, but at locations "far away" from any of the nuclei in the system.
Prediction of when a solvated electron will occur remains challenging, to the best of my knowledge.  One potential method for their theoretical prediction/explanation is by a search for "non-nuclear attractors" (NNAs) in the electron density, using methods such as the QTAIM of Bader$^\ddagger$.  (QTAIM studies the spatial distribution of the electron density and its derivatives, mainly the gradient and Laplacian.)  Attractors in QTAIM are "concentrations" of electron density that most frequently occur at atoms (nuclear attractors), but sometimes are observed far from atoms (non-nuclear attractors). Thus, the presence of an NNA in an electride system provides a reasonable guess for the location of the potential well(s) holding the 'independent' electron.  However, in some electride systems no NNAs are apparent, so the absence of an NNA is not diagnostic of a non-electride system (see, e.g., the post and comment thread here).
More generally, research into solvated electrons is quite active, including work on excited states:

Electronically excited states in size selected solvated alkali metal atoms III: Depletion Spectroscopy of $\ce{Na(NH3)}_n$-Clusters
Preprint of a 1998 paper $-$ PDF link
Electron solvation dynamics in $\ce{I^- (NH3)}_n$ clusters
Faraday Discuss 115: 49 (2000) $-$ doi:10.1039/a909865h $-$ PDF link
Dynamics of Electron Solvation in Molecular Clusters
Acc Chem Res 42(6): 769 (2009) $-$ doi:10.1021/ar800263z $-$ PDF link
Time-Resolved Excited State Energetics of the Solvated Electron in Sodium-Doped Water Clusters
J Phys Chem A 118(37): 8517 (2014) $-$ doi:10.1021/jp502238c
Dynamics of electron solvation in methanol: Excited state relaxation and generation by charge-transfer-to-solvent
J Chem Phys 142: 234501 (2015) $-$ doi:10.1063/1.4922441
$-$ PDF link

Others can be easily found by searching for, e.g., 'excited states of solvated electrons' $-$ for full-text PDFs only, in Google you can add the filetype:pdf flag to the end of the search string.
$^\dagger$G. Herzberg, Atomic Spectra and Atomic Structure. 2nd Dover Edition, 2010. (Amazon)
$^\ddagger$R.W.F. Bader Chem Rev 91: 893 (1991). doi:10.1021/cr00005a012

