For the roux, in a heavy 2-quart saucepan stir together the flour and oil until smooth. Cook over medium-high heat for 5 minutes, stirring constantly. Reduce heat to medium. Cook and stir constantly about 15 minutes more or until a dark, reddish-brown roux forms. Cool.
In a 3-1/2-, 4-, or 5-quart crockery cooker place water. Stir in roux. Add sausage, chicken, okra, onion, sweet pepper, celery, garlic, salt, pepper, and ground red pepper.
Cover; cook on low-heat setting for 6 to 7 hours or on high-heat setting for 3 to 3-1/2 hours. Skim off fat. Serve over the hot cooked rice.