For roux: In a heavy sauce pan, cook flour over medium heat about 6 minutes or until brown, still occasionally. Remove from heat; cool slightly. Gradually stir broth into flour. Cook and stir until thickened and bubbly.
Pour thickened flour mixture in a 3 1/2 or 4-quart slow cooker.
Add chicken, sausage, okra, the water, onion, sweet pepper, celery, garlic, thyme, 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.