If Audition can open and play the file format and you are unsure what to do next, feel free to ask advice. I'll try to help.
To make the files "FLAC compatible" you must save them in the 24-bit integer format (or lower).
Once you are there you might also lower the sample rate. 192 kHz is overkill for anything. Actually, also 24-bit is overkill, especially for vinyl sourced audio. The real dynamic range and S/N ratio of vinyl recordings is nowhere near even "16-bit" (which can store 0 ... -96 dBFS, and even more in the audible frequency range if dithering and noise shaping is applied.)
I probably would "remaster" the files to the standard CD Audio format (2 ch/16-bit/44.1 kHz). They would be universally compatible without sacrificing the audible quality (if the conversion is done properly).