In a skillet, heat oil over medium heat. Whisk in flour and cook, stirring constantly, until deep brown (10–15 minutes).
Transfer roux to the crockpot.
Add onion, bell pepper, celery, garlic, chicken, sausage, broth, tomatoes, and seasonings. Stir well.
Cover and cook on LOW for 6–8 hours or HIGH for 4 hours.
About 30 minutes before serving, stir in okra.
Remove chicken, shred, and return to the pot.
Adjust seasoning and garnish with parsley and green onions.