Heat a medium skillet over medium-high heat; add flour. Toast, stirring frequently, until deep golden brown, about 5 minutes. Transfer to a plate to stop it from cooking.
Heat oil in a large Dutch oven over medium-high heat. Add sausage and cook, stirring often, until browned, about 5 minutes. Remove with a slotted spoon, transfer to a large bowl, and reserve. Add the chicken, and brown, turning once, about 5 minutes. Remove with a slotted spoon, and add to the bowl with the sausage. Add the pepper, onion, and celery to the Dutch oven. Season with salt and pepper, and cook until softened, about 4 minutes. Remove with a slotted spoon, and add to the sausage and chicken.
Reduce heat to medium-low, and add the butter to the Dutch oven. Once melted, sprinkle in the toasted flour, and stir until combined. Continue cooking until bubbles form and mixture becomes very thick and dark brown, about 4 minutes. Add the stock, tomatoes, okra, thyme, bay leaf, and reserved meat and vegetables. Raise heat and bring to a boil; let simmer, uncovered, until chicken is tender and liquid has thickened, about 1 1/4 hours. Remove thyme, and serve hot over rice.