Combine the flour, salt, Cayenne pepper and paprika in a flat bowl. Thoroughly coat the chicken pieces on all sides, then place in a container to refrigerate for at least one hour.
Melt the butter with the black pepper, hot sauce, and garlic powder in a small saucepan over moderate heat. Reduce heat to keep warm while you fry the chicken wings.
Deep-fry the chicken wings and drumlets, 10 pieces at a time, in 375° oil for about 13 minutes. Drain on paper towels for 20 seconds and immediately place fried chicken pieces in a plastic bowl with a tight-fitting cover.
Pour half the hot sauce mixture over the first 10 pieces of chicken. Cover tightly and toss to coat. Repeat the process with the remaining ingredients.
Serve warm with ranch or blue cheese dressing as a dip - and with plenty of napkins.
Wings can be prepared in advance and frozen, then reheated in a 400° oven for 10 minutes.