In a shallow, non-aluminum dish, combine first 5 ingredients. Add chicken and toss once to coat. Cover and chill 8 hours or overnight, turning once or twice.
Place pieces on rack to drain slightly but do not pat dry.
In a paper bag, combine flour, salt, black pepper, and red pepper. Toss chicken in flour mixture and place on a clean rack or a baking sheet. Toss each piece again, shake off excess flour and set aside at cool room temperature for 2 hours.
In 2 large, heavy skillets, or 1 electric skillet, heat enough oil to reach a depth of 1/2-inch to 350 to 360 degrees. Add chicken pieces to the hot oil one by one. (Note: Adding too many pieces at once lowers the temperature of the oil and the chicken will not brown properly.) Adjust temperature so oil remains between 300 and 320 degrees. Cook, turning once with tongs, 10 to 12 minutes per side (4 to 5 minutes for boneless breasts) or until juices run clear when pierced in the thickest part. (Thicker pieces may require more cooking time.) Transfer pieces as they are done to paper towels to drain. Serve hot or warm.
Gravy for Fried Chicken
Drain all the oil from the cooking skillet through a sieve and into a bowl. Return the skillet to medium heat. Add two tablespoons of the chicken-frying fat to the skillet, along with any browned bits caught by the strainer. Add two tablespoons of flour, blend well, and cook for two minutes, stirring. Off heat, add a scant two cups boiling chicken stock. Simmer for 2 minutes, season (using freshly grated nutmeg, if desired) and serve.