Chrome 56+ / Firefox 52+
Might not work on all OSes
Add the following to /usr/lib/plexmediaserver/Resources/Profiles/Web.xml
within the <Client>
section:
<DirectPlayProfiles>
<MusicProfile container="flac" codec="flac" />
</DirectPlayProfiles>
Included my Web.xml as an example. I just added <DirectPlayProfiles>
to Plex Media Server 1.5.5.3634 stock Web.xml.