Cook and stir flour in a large, heavy pot over medium-low heat until flour turns golden brown, about 15 minutes. Pour browned flour into a bowl and return pot to heat.
Increase heat to medium and add oil to the pot. Cook and stir onions and bell peppers in hot oil until slightly softened, about 7 minutes.
Stir garlic, thyme, and bay leaves into onion mixture; cook and stir for 1 minute. Add sausage to onion mixture and cook and stir until browned and crumbly, 5 to 10 minutes.
Stir diced tomatoes with juice, shredded chicken, chicken broth, vegetable juice cocktail, browned flour, and Creole seasoning into sausage mixture. Bring to a boil, reduce heat to low, cover the pot, and simmer, stirring often, until mixture is hot and flavors blend, 20 to 30 minutes.
Pour shrimp into sausage-chicken mixture; bring to a simmer. Cook shrimp until they are pink on the outside and the meat is no longer transparent in the center, about 5 minutes.
Discard bay leaves. Season gumbo with salt and pepper to taste.