Place flounder and cayenne pepper sauce in a large resealable plastic bag. Let marinate in the refrigerator, at least 1 hour.
Place corn flour in a shallow pan. Remove fillets, reserving marinade in the bag, and carefully dredge in the corn flour one at a time, coating completely and transferring to a plate.
Dip each coated fillet back into the marinade, dredge again in corn flour, and dip in the marinade again. Repeat with remaining fillets.
Heat butter and olive in a large nonstick skillet over medium-high heat until sizzling. Arrange fillets in the skillet so they are not touching and cook until golden brown, about 3 minutes. Flip fillets carefully with a wide, nonstick spatula and cook until second side is browned, about 3 minutes more. Serve with blue cheese dressing.