The Jun Suzuki credited on the Final Fantasy soundtrack and the one credited on the FLCL soundtracks are different persons.
This profile belongs to the Jun Suzuki (鈴木准) credited as tenor on the Final Fantasy VIII soundtrack.
I created a profile page
here for the other Jun Suzuki (鈴木淳), who plays bass as a support member for Japanese band the pillows among other things.
This one should be linked to the FLCL soundtracks 1 & 2 (maybe all three, but I have no source to confirm whether he's actually credited on the third soundtrack or not, although he most likely is).