Sprinkle chicken pieces with salt and pepper; place them in a deep-sided baking dish.

Whisk buttermilk, hot pepper sauce, and 1 teaspoon cayenne pepper together in a large bowl; pour over chicken, tossing to coat all sides. Cover the dish with plastic wrap; marinate in the refrigerator for about 2 hours.

Remove chicken from buttermilk mixture; shake off excess. Discard remaining buttermilk mixture.

Place flour, 1 tablespoon cayenne pepper, garlic powder, paprika, salt, and pepper in a large resealable plastic bag; shake well to combine. Place 2 or 3 pieces of chicken at a time into the plastic bag and shake well to coat chicken pieces with seasoned flour.

Heat oil in a deep fryer or large saucepan to 350 degrees F (175 degrees C).

Gently place chicken pieces into hot oil and fry until chicken is cooked through and golden brown, about 8 to10 minutes for breasts and wings, and 13 to 15 minutes for thighs and drumsticks. An instant-read thermometer inserted into the center should read at least 165 degrees F (74 degrees C). Drain fried chicken on paper towels.