Place the chicken pieces in a large bowl. Pour the buttermilk and hot sauce over them, toss to coat, then cover and refrigerate for at least 2 hours or overnight.
In a large shallow dish, whisk together the gluten free flour blend, cornstarch, garlic powder, onion powder, smoked paprika, cayenne pepper, salt, and black pepper.
Remove one piece of chicken from the buttermilk, letting excess drip off. Dredge it in the flour mixture, pressing firmly to coat. Drizzle a few drops of the buttermilk over the flour on the chicken and press again to create craggy, crispy bits. Set on a wire rack and repeat with remaining pieces. Let them rest for 15 minutes.
Fill a large heavy-bottomed pot or Dutch oven with about 2 inches of vegetable oil and heat to 325 degrees F. Use a thermometer to monitor the temperature.
Working in batches of 3 to 4 pieces so the oil temperature stays steady, carefully lower the chicken into the hot oil. Fry for 6 to 7 minutes per side for thighs and drumsticks, or 7 to 8 minutes per side for breasts, until the coating is deep golden brown and the internal temperature reaches 165 degrees F.
Transfer the fried chicken to a wire rack set over a sheet pan. Season lightly with a pinch of salt while still hot. Let rest for 5 minutes before serving.