Preheat oven to 425°F. Mist bottom of a large baking dish with nonstick cooking spray. Combine panko, Parmesan and butter in a small bowl and stir mixture well.
Sprinkle both sides of flounder generously with salt and pepper. Arrange fish in prepared baking dish. Sprinkle panko-Parmesan mixture over fish. Bake until fish is cooked through and crumbs are golden, about 15 minutes. Serve immediately.