Make the roux by heating the flour and oil in a small saucepan or skillet over medium heat. Cook for 8-10 minutes, whisking constantly so that it doesn’t burn. The mixture should turn a light reddish-brown. If it starts to get dark too quickly, reduce the heat to medium-low.
Transfer the roux to the bottom of a slow cooker.
Add the chicken, and then top with the sausage, tomatoes, onion, bell pepper, celery, garlic, bay leaf, Creole seasoning, paprika, thyme, oregano, and chicken broth.
Cover and cook on LOW for 6-8 hours, on HIGH for 3-4 hours, or until the chicken is cooked through and the vegetables are tender.
Turn the slow cooker to the HIGH setting (if it’s not already there), and stir in the shrimp. Cover and cook on HIGH for 15-20 more minutes (stirring twice), or until shrimp are pink.
Discard the bay leaf. Remove the chicken from the pot. Chop or shred the meat, and then return the chicken to the pot. Stir in the green onions and parsley.
Taste and season with salt and pepper, cayenne, or hot sauce. Serve over rice and garnish with additional chopped fresh parsley, if desired.