HERE'S THE OFFICIAL NYS LAW;
"Summer flounder may not have heads or tails removed or be otherwise cleaned, cut, filleted, or skinned until brought to shore, with the following exception: the white side fillet or white skin only of a legal size fluke may be removed to use as bait. The carcass of the fluke with dark side completely intact must be retained for inspection of size limit and counts against the possession limit."
To summarize, you can only use the white belly, not the dark side. The carcass must be with you.