Our Southern Flounder have large mouths but I've seen pics of other Flatfish that are common to other regions having very small mouths. For our large-mouthed Southerns, a Stingray Grub, 4" Finesse Worm, 4" Curltail, 3"-4" Swim, hopped along Bottom in ALL Suspect Areas. For a jighead, I like some 1/16 oz., use mostly 1/8 oz. for this job though...1/4 oz. or more would be used strictly out of necessity...all 'heads with 3/0 and 4/0 hooks.
Now, for those Flatties with smaller mouths, I would be throwing Panfish or near-Panfish-sized plastics. Something skinny, narrow...vary color by Water Clarity. Those fish know what might fit in their mouth...and they're not always there and willing. I would do these things, keep colors simple, and marinate in a Scent Oil that "are aimed at" their Common Forage/Local Fare (to help them commit as they sneak up behind the bait, or hold on long enough to tell You they're there).
Shoot a transluscent Natural color, a more opaque/Dark Natural color, a Dark/Black color, a Purple color, and a bright color that might be Pink or Chartreuse or other loud color You've learned to be productive.