I stumbled upon a helpful CSS-tricks article addressing this specific issue. The recommended approach outlined in the article is as follows:
display: -webkit-box; /* OLD - iOS 6-, Safari 3.1-6 */
display: -moz-box; /* OLD - Firefox 19- (buggy but mostly works) */
display: -ms-flexbox; /* TWEENER - IE 10 */
display: -webkit-flex; /* NEW - Chrome */
display: flex; /* NEW, Spec - Opera 12.1, Firefox 20+ */
-webkit-box-flex: 1; /* OLD - iOS 6-, Safari 3.1-6 */
-moz-box-flex: 1; /* OLD - Firefox 19- */
width: 20%; /* For old syntax, otherwise collapses. */
-webkit-flex: 1; /* Chrome */
-ms-flex: 1; /* IE 10 */
flex: 1; /* NEW, Spec - Opera 12.1, Firefox 20+ */