Definitely sure. It supported it just marginally enough to mangle it in a way that you couldn't work around. My fix was to literally check if the floating sidebar overlapped the content and, if so, add a css class to the body that I could use to fix the pagespeed insights browser.
I'll give the Mobile Friendly Test a shot with and without the hack.
Edit: Yup, still busted. And the new test is broken as well (probably using the same backend). This is what it looks like: http://imgur.com/fBIP80y
I run a popular site that heavily uses flexboxes, with dozens of flex containers on every page, different alignments, etc. I just checked pagespeed insights, and the site renders fine in the little mobile phone preview from your image, so it's definitely supported. Check your code, it might be incorrect, you might need webkit prefixes, or you might be using outdated flexbox specs that have been dropped.
I'll give the Mobile Friendly Test a shot with and without the hack.
Edit: Yup, still busted. And the new test is broken as well (probably using the same backend). This is what it looks like: http://imgur.com/fBIP80y