If I understand correctly, you want flex-2-child to fill the height and width of its parent, so that the red area is fully covered by the green?
If so, you just need to set flex-2 to use Flexbox:
.flex-2 {
display: flex;
}
Then tell flex-2-child to become flexible:
.flex-2-child {
flex: 1;
}
See http://jsfiddle.net/2ZDuE/10/
The reason is that flex-2-child is not a Flexbox item, but its parent is.