For roux, in a medium heavy saucepan stir together flour and oil until smooth. Cook and stir constantly over medium-high heat for 5 minutes. Reduce heat to medium. Cook and stir constantly about 15 minutes more or until a dark, reddish brown color is reached; cool.
Place water in a 3-1/2- or 4-quart slow cooker. Stir in roux. Add sausage, chicken, okra, onion, sweet pepper, celery, garlic, salt, black pepper, and cayenne pepper.
Cover and 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 gumbo over hot cooked rice. Makes 6 servings.