The LHS flex child in this example has 1em padding, and it will cause RHS to overflow the parent:
I had similar problems with flexbox and box-sizing: border-box;. The latter one just doesn't seem to work in IE. Width wouldn't work in this case since padding will change it - but if you can use max-width, that should fix the problem.
flexbox
box-sizing: border-box;
max-width