Mix together flour, paprika, cayenne pepper, and salt in a small bowl. Place chicken wings in a large dish and sprinkle flour mixture over them until well coated. Place on baking sheet and refrigerate for 1 hour, uncovered.
Preheat oven to 400 degrees F (204 degrees C).
Bake wings in preheated oven until no longer pink at the bone and juices run clear, about 15 minutes per side.
Combine butter, hot sauce, pepper, and garlic in a small saucepan over low heat. Cook and stir until butter is melted and mixture is well blended, about 3 minutes. Place chicken wings in serving bowl and add hot sauce mixture, mixing well.