Combine thighs, buttermilk, and 1 teaspoon salt; refrigerate 2 to 8 hours.
Whisk rice flour, all-purpose flour, paprika, thyme, garlic powder, cayenne, white pepper, and remaining salt in a shallow pan.
Shake excess buttermilk from thighs; press into flour mixture. Rest coated chicken 10 minutes.
Heat 1 1/2 inches peanut oil in a heavy pot to 340°F.
Fry thighs in two batches, 5 to 7 minutes per side, maintaining oil at 330°F to 345°F.
Remove when coating is copper brown and center reaches 165°F. Drain on a wire rack.
Rest 6 minutes to finish crisping crust.