CSS align one item right with flexbox

To align one flex child to the right set it withmargin-left: auto;

From the flex spec:

One use of auto margins in the main axis is to separate flex items into distinct "groups". The following example shows how to use this to reproduce a common UI pattern - a single bar of actions with some aligned on the left and others aligned on the right.

.wrap div:last-child {
  margin-left: auto;
}

Updated fiddle

.wrap {
  display: flex;
  background: #ccc;
  width: 100%;
  justify-content: space-between;
}
.wrap div:last-child {
  margin-left: auto;
}
.result {
  background: #ccc;
  margin-top: 20px;
}
.result:after {
  content: '';
  display: table;
  clear: both;
}
.result div {
  float: left;
}
.result div:last-child {
  float: right;
}

<div class="wrap">
  <div>One</div>
  <div>Two</div>
  <div>Three</div>
</div>

<!-- DESIRED RESULT -->
<div class="result">
  <div>One</div>
  <div>Two</div>
  <div>Three</div>
</div>

Note:

You could achieve a similar effect by setting flex-grow:1 on the middle flex item (or shorthand flex:1) which would push the last item all the way to the right. (Demo)

The obvious difference however is that the middle item becomes bigger than it may need to be. Add a border to the flex items to see the difference.

Demo

.wrap {
  display: flex;
  background: #ccc;
  width: 100%;
  justify-content: space-between;
}
.wrap div {
  border: 3px solid tomato;
}
.margin div:last-child {
  margin-left: auto;
}
.grow div:nth-child(2) {
  flex: 1;
}
.result {
  background: #ccc;
  margin-top: 20px;
}
.result:after {
  content: '';
  display: table;
  clear: both;
}
.result div {
  float: left;
}
.result div:last-child {
  float: right;
}

<div class="wrap margin">
  <div>One</div>
  <div>Two</div>
  <div>Three</div>
</div>

<div class="wrap grow">
  <div>One</div>
  <div>Two</div>
  <div>Three</div>
</div>

<!-- DESIRED RESULT -->
<div class="result">
  <div>One</div>
  <div>Two</div>
  <div>Three</div>
</div>

For a terse, pure flexbox option, group the left-aligned items and the right-aligned items:

<div class="wrap">
  <div>
    <span>One</span>
    <span>Two</span>
  </div>
  <div>Three</div>
</div>

and use space-between:

.wrap {
  display: flex;
  background: #ccc;
  justify-content: space-between;
}

This way you can group multiple items to the right(or just one).

https://jsfiddle.net/c9mkewwv/3/

To align some elements (headerElement) in the center and the last element to the right (headerEnd).

.headerElement {
    margin-right: 5%;
    margin-left: 5%;
}
.headerEnd{
    margin-left: auto;
}