For the honey butter: Combine the butter, honey and salt in the bowl of a stand mixer fitted with the whisk attachment and whip on medium speed until the butter is well-mixed, about 2 minutes. Taste and adjust the salt and honey to your preference. Store the honey butter in the refrigerator. (Bring to room temperature before serving.)
For the brined chicken: Combine the salt, sugar, chile flakes and lemon and orange peels with 1 gallon water in a large pot and heat over medium heat, stirring, until the sugar and salt dissolve. Cool completely.
For the fried chicken: Stir together the flour, rice flour, garlic powder, black pepper, onion powder, baking powder, cayenne pepper, 3 teaspoons salt, and 1/4 teaspoon smoked paprika. Taste it-it should taste good!
Divide the flour mixture between two deep containers. Pour the buttermilk into a third container.
Batter each piece of chicken one at a time: Dip a piece into the first flour container and coat lightly with the flour mixture. Then submerge the chicken in the buttermilk. Lift the chicken out of the buttermilk, and let the excess drip off; place into the second flour mixture to coat the chicken again. (Be careful to ensure that the chicken is evenly and fully coated, but do not let the coating become too thick.) Place the battered chicken onto a plate and proceed with the remaining chicken.
Let the chicken rest, battered, while heating the oil. If you are not going to fry the chicken within 1 hour, place in the refrigerator, uncovered, for up to 3 hours. If you refrigerate the battered chicken, be sure to bring it to room temperature for 30 minutes before frying.
Fill a sturdy, high-sided pot with four inches of oil and preheat the oil over medium heat. Using a frying thermometer, carefully bring the oil to 340 degrees F. Set a wire rack over a cookie sheet.
Place several pieces of the chicken in the oil (do not crowd; fry in 2 batches if necessary). If you place too much chicken into the oil, the temperature will drop too much and the chicken will become greasy. Carefully adjust the heat to keep the oil at a consistent temperature of 315 to 320 degrees F. Fry the chicken until an instant-read thermometer inserted into the thickest point of the meat reads at least 165 degrees F, 11 to 13 minutes for the drumsticks and about 10 minutes for the breasts and thighs. Transfer the cooked chicken to the wire rack.
Sprinkle the top of the just-fried chicken with salt and some of the remaining tablespoon smoked paprika. Let rest 1 minute, then flip the chicken and sprinkle the other side with salt and smoked paprika. Serve with room temperature honey butter to spread onto the hot fried chicken.