Place broiler-fryer in a Dutch oven; cover with water. Bring to a boil; cover, reduce heat, and simmer 1 hour. Remove chicken, reserving 9 cups broth. Bone and chop chicken.
Combine flour and oil in a Dutch oven; cook over medium heat, stirring constantly, until mixture is chocolate colored (about 30 minutes).
Add 2 cups onion and next 4 ingredients; saute 5 minutes or until tender. Add salt and next 6 ingredients; saute 2 minutes. Add reserved 9 cups broth, chicken, okra, tomato paste, and sausage. Bring to a boil; cover, reduce heat, and simmer 1 1/2 hours, stirring occasionally. Discard bay leaves.
Peel and devein shrimp. Add shrimp and oysters to broth mixture; simmer an additional 10 minutes or until shrimp turn pink and edges of oysters begin to curl. Serve over rice.