There appears to be support for flac, as you can see here: https://github.com/Fyrd/caniuse/blob/HEAD/features-json/flac.json
See also #2185 which has added support for FLAC.
But flac does not show up in the main website.
Neither with a search: http://caniuse.com/#search=flac
Nor with an attempt to get a direct link: http://caniuse.com/#feat=flac
Firefox 51 is adding support for FLAC:
https://bugzilla.mozilla.org/show_bug.cgi?id=1195723
It would be good to start keeping track of this feature.
The data's currently still incomplete and pending review, which is why it isn't on the site yet (and until now there hadn't been any requests to show it)
+1
Its coming to chrom{e,ium} as well: https://bugs.chromium.org/p/chromium/issues/detail?id=93887
As now mentioned in https://bugs.chromium.org/p/chromium/issues/detail?id=93887, Chrome 56+ will support FLAC.
For the record: https://9to5google.com/2017/01/12/chrome-56-flac-playback/
Firefox 51 with support for FLAC is now stable: https://www.mozilla.org/en-US/firefox/51.0/releasenotes/
Now available at http://caniuse.com/#feat=flac
Most helpful comment
Firefox 51 is adding support for FLAC:
https://bugzilla.mozilla.org/show_bug.cgi?id=1195723
It would be good to start keeping track of this feature.