Preheat the oven to 375 degrees F.
Line a baking sheet with parchment and grease the paper with butter. Rinse the flounder; pat dry with paper towels. Place the fish on the prepared baking sheet with head-side up.
Starting on one side of the fish, insert a knife horizontally into the slit. Begin cutting, about 1 inch from the head, between the flesh and bone, stopping just before the tail to form a pocket. Cut another pocket on the opposite side of the fish.
Combine the crabmeat, saltines, mayonnaise, parsley, egg, green onion and Old Bay Seasoning in a medium bowl and fold together. Spoon the mixture evenly into the prepared fish pockets.
Sprinkle the fish with the bread crumbs and drizzle with the melted butter. Bake until the fish flakes easily when tested with fork, about 25 minutes.