Season chicken with salt and black pepper. Combine flour and red pepper; set aside. Combine egg and milk; dip chicken in egg mixture and dredge in flour mixture, coating chicken well. Pour oil to a depth of one inch in a heavy 10" to 12" skillet; heat oil to 350°.
Fry chicken in hot oil over medium heat 15 to 20 minutes or until golden, turning occasionally. Remove small pieces earlier, if necessary, to prevent overbrowning. Drain chicken on paper towels, reserving 1/4 cup drippings in skillet for Cream Gravy. Serve with gravy.
Heat pan drippings in skillet over medium heat. Add flour, stirring until browned. Gradually add hot milk; cook, stirring constantly until thick and bubbly. Add salt, black pepper and red pepper. Serve hot.