Well, I think this is short and more descriptive:
"Burrrn uses cdrdao for burning audio CDs from compressed audio files. It can read all type of tags from the supported formats (wav, mp3, mpc, ogg, aac, ape, flac and cue sheets), and burn them as CD-Text."
About CDex, yes, it supports FLAC, of course.

-Go to Configuration/Encoder/Select External encoder
-Encoder path: Search flac.exe
-Parameter string (you can add tags using something like this): %1 -o %2 --tag=Title="%t" --tag=Artist="%a" --tag=Album="%b" --tag=Track="%tn" --tag=Genre="%g" --tag=Date="%y"
-Bitrate: If you want to set 32 Kbps... but it doesn't work with FLAC.
-File Extension: flac
That's all. You could save this configuration as "Profile", and it'll be ready for future uses.