Completely removing the backbone of an odd-shaped fish like a flounder sounds like an impossible task, but Vern Becnel has mastered it.
In addition to a narrow-bladed knife, he uses a pair of stainless steel toe nail snips that can be purchased at any drug store.
Try this; it is easier than it looks.
1.) After de-heading and gutting the flounder, make a cut to the backbone the length of the fish down the center line of the dark side of the fish.
4.) After folding both flaps aside for better vision, insert the knife beneath the backbone of the fish and above the flesh on the bottom of the fish. Cut in both directions as far to the edges as possible and as deep as the knife will go to loosen the backbone from the flesh.