Q:

How to center a flex container but left-align flex items

I want the flex items to be centered but when we have a second line, to have 5 (from image below) under 1 and not centered in the parent.

Here's an example of what I have:

ul {
  display: flex;
  flex-direction: row;
  flex-wrap: wrap;
  justify-content: center;
  margin: 0;
  padding: 0;
}
li {
  list-style-type: none;
  border: 1px solid gray;
  margin: 15px;
  padding: 5px;
  width: 200px;
}
<ul>
  <li>1</li>
  <li>2</li>
  <li>3</li>
  <li>4</li>
  <li>5</li>
  <li>6</li>
</ul>

http://jsfiddle.net/8jqbjese/2/

A:

Flexbox Challenge & Limitation
The challenge is to center a group of flex items and left-align them on wrap. But unless there is a fixed number of boxes per row, and each box is fixed-width, this is currently not possible with flexbox.
Using the code posted in the question, we could create a new flex container that wraps the current flex container (ul), which would allow us to center the ul with justify-content: center. 
Then the flex items of the ul could be left-aligned with justify-content: flex-start.
#container {
    display: flex;
    justify-content: center;
}

ul {
    display: flex;
    justify-content: flex-start;
}

This creates a centered group of left-aligned flex items.
The problem with this method is that at certain screen sizes there will be a gap on the right of the ul, making it no longer appear centered.

This happens because in flex layout (and, actually, CSS in general) the container:

doesn't know when an element wraps;
doesn't know that a previously occupied space is now empty, and
doesn't recalculate its width to shrink-wrap the narrower layout.

The maximum length of the whitespace on the right is the length of the flex item that the container was expecting to be there.
In the following demo, by re-sizing the window horizontally, you can see the whitespace come and go.
DEMO

A More Practical Approach
The desired layout can be achieved without flexbox using inline-block and  media queries.
HTML
<ul>
    <li>1</li>
    <li>2</li>
    <li>3</li>
    <li>4</li>
    <li>5</li>
    <li>6</li>
</ul>

CSS
ul {
    margin: 0 auto;                  /* center container */
    width: 1200px;
    padding-left: 0;                 /* remove list padding */
    font-size: 0;                    /* remove inline-block white space;
                                        see https://stackoverflow.com/a/32801275/3597276 */
}

li {
    display: inline-block;
    font-size: 18px;                 /* restore font size removed in container */
    list-style-type: none;
    width: 150px;
    height: 50px;
    line-height: 50px;
    margin: 15px 25px;
    box-sizing: border-box;
    text-align: center;
}

@media screen and (max-width: 430px) { ul { width: 200px; } }
@media screen and (min-width: 431px) and (max-width: 630px) { ul { width: 400px; } }
@media screen and (min-width: 631px) and (max-width: 830px) { ul { width:600px;  } }
@media screen and (min-width: 831px) and (max-width: 1030px) { ul { width: 800px; } }
@media screen and (min-width: 1031px) and (max-width: 1230px) { ul { width: 1000px; } }

The above code renders a horizontally-centered container with left-aligned child elements like this:

DEMO

Other Options

Properly sizing and aligning the flex item(s) on the last row
Desandro Masonry

Masonry is a JavaScript grid layout library. It
  works by placing elements in optimal position based on available
  vertical space, sort of like a mason fitting stones in a wall. You’ve
  probably seen it in use all over the Internet.
source: http://masonry.desandro.com/

CSS Grid Layout Module Level 1

This CSS module defines a two-dimensional grid-based layout system, optimized for user interface design. In the grid layout model, the children of a grid container can be positioned into arbitrary slots in a predefined flexible or fixed-size layout grid.
source: https://drafts.csswg.org/css-grid/

A:

You can achieve it with CSS Grid, just use repeat(autofit, minmax(width-of-the-element, max-content))

ul {
       display: grid;
       grid-template-columns: repeat(auto-fit, minmax(210px, max-content));
       grid-gap: 16px;
       justify-content: center;
       padding: initial;
}

li {
    list-style-type: none;
    border: 1px solid gray;
    padding: 5px;
    width: 210px;
}
<ul>
    <li>1</li>
    <li>2</li>
    <li>3</li>
    <li>4</li>
    <li>5</li>
    <li>6</li>
    <li>7</li>
</ul>

http://jsfiddle.net/rwa20jkh/

