The "Supported File Types" setting specifies the file types that the target device supports. I just leave that set to "*" when syncing MP3 files. I guess if you were syncing FLAC and MP3 files it would make sense to set it to MP3 for a device that can only play MP3s.
If your FLAC files have now synced and were converted to MP3s, I suspect with the trying different things that MC has got a little out of whack. A resync should copy the MP3s over as well, if they aren't in the folder already.
Try setting up to do a new sync, set all the options including setting the Audio Mode to "Specified output format only when necessary", with the supported format as MP3, then click OK and check if there are any files marked as "In Queue" still. If not, click the "Recheck Sync" button which will basically check everything, but often forces all files to be synced again, depending on other settings.
Of course, if your MP3 source files are marked as "On Device" then MC thinks it has already copied the files across to the folder. If that isn't correct, remove the playlist from the settings (add a dummy one file playlist if necessary to get all the option settings), then make sure the "Delete from handheld any files not in sync list" setting is ticked, then sync, then add your playlist back, then sync.
If nothing works, delete the Device (just select it in the left navigation pane and press the Delete button - don't use the right click "Remove & Ignore Device" function) and start again.
Basically, the Handheld sync functionality works, but it can be a bit tricky to get set up and working properly.
https://wiki.jriver.com/index.php/Sync_Handheldhttps://wiki.jriver.com/index.php/Handheld_Sync_Options