Heat vegetable oil over medium heat in a large stock pot. Add garlic, celery, bell peppers, onion, oregano, Creole seasoning, and pepper. Cook, stirring occasionally, until vegetables are crisp-tender, about 10 minutes.
Sprinkle flour over vegetable mixture and mix well. Cook until golden brown, about 5 minutes.
Pour in chicken stock, water, rice, okra, sausage, tomatoes, and hot sauce. Bring to a boil; reduce heat and simmer until sausage is heated through and vegetables are tender, about 5 minutes. Stir in cooked chicken and heat through, about 5 minutes more. Adjust seasonings to taste.