I rebuilt my personal site on Flexbox in December last year after making the call that it was widely supported enough [1]. There were a few hiccups:
1. Safari's requirement to use the webkit- prefix is a pain. Thankfully there are SASS libraries that work around that [2], but you aren't using Flexbox directly.
2. Google's pagespeed tools doesn't support it. It's an ancient version of Webkit -- your mobile score will suffer. If that matters to you, you'll have to do some hacking to ensure that it doesn't affect things on the mobile side.
[1] for a personal site.