Input group with flex box
Unless you're overwriting properties set elsewhere, there's no reason for this line because this is the default for all flex containers:

flex-flow: row nowrap;


If your goal is to make this work on browsers with either of the old Flexbox implementations, there are 2 things to be aware of:


The March 2012 draft (IE10) does not have individual properties for flex-grow, flex-shrink, or flex-basis.  The only way to control them is via the flex shorthand.
The original draft does not allow you to have differing flex-shrink and flex-grow values.  It would be ok to translate flex: 1 1 auto to box-flex: 1, but you can't translate something like flex: 1 0 (with prefixes).  For your purpose, box-flex: 0 should work (though you might have problems with buttons in old Webkit browsers, see: https://stackoverflow.com/questions/16961192/flexbox-doesnt-work-with-buttons).