Toss the chicken, buttermilk and 1 teaspoon salt in a bowl. Cover and refrigerate, 1 hour.
Heat 1 inch of vegetable oil in a large deep skillet over medium-high heat until a deep-fry thermometer registers 360.
Mix the flour, paprika, 1/4 teaspoon pepper and the garlic powder in a shallow bowl. Remove the dark meat from the buttermilk, shake off the excess and roll in the flour mixture. Shake off the excess flour, place in the hot oil and fry, turning occasionally, until golden brown and cooked through, about 15 minutes (adjust the heat as needed). Drain on paper towels.
Reheat the oil to 360 degrees F. Repeat with the chicken breasts and wings, frying for about 15 minutes. Serve hot or at room temperature.