On a plate, combine the white rice flour, salt, and pepper. Place the lightly beaten egg on a plate. Spread the potato flakes out on another plate.
Dip both sides of each tilapia fillet in flour mixture, then egg, then potato flakes.
In a large skillet, heat oil and melt butter together over medium-high heat. Brown the tilapia fillets for about 3 minutes per side, or until browned and fish flakes easily with a fork.