Sprinkle chicken with salt and pepper; dredge in flour. Set 3 tablespoons flour aside.
Heat oil to 375° in a 10-inch cast-iron skillet. Brown 4 chicken pieces for 12 to 15 minutes. Drain well on paper towels. Repeat procedure with remaining chicken.
Drain oil from skillet, reserving 3 tablespoons pan drippings in skillet. Add reserved flour to pan drippings, stirring until smooth. Cook 1 minute, stirring constantly. Gradually add milk to mixture in skillet; cook over medium heat, stirring constantly, until thickened and bubbly. Serve gravy with chicken and hot cooked rice.