Place flour in a large Dutch oven over medium heat; cook 20 minutes or until light brown, stirring constantly with a whisk. (If flour browns too fast, remove pan from heat; stir constantly until it cools down.) Remove flour from pan, and set aside.
Add oil to pan. Stir in onion, bell pepper, and celery; cook 10 minutes or until onion is tender, stirring frequently. Stir in garlic; cook 30 seconds. Remove onion mixture from pan; set aside.
Increase heat to medium-high; add chicken and sausage to pan. Cook 4 minutes or until chicken is done; return onion mixture to pan. Remove pan from heat. Sprinkle reserved flour over chicken mixture; stir well. Return pan to medium heat. Drain 1 can tomatoes; stir in 1 can drained tomatoes and 1 can undrained tomatoes. Cook 2 minutes, stirring constantly. Add broth, Worcestershire, and bay leaves; bring to a boil, stirring constantly. Cover, reduce heat, and simmer 30 minutes, stirring occasionally. Discard bay leaves. Stir in salt, black pepper, and hot sauce. Serve over rice.