Heat a large Dutch oven over medium-high heat. Coat pan with cooking spray. Add 1 teaspoon oil, chicken, and sausage; sauté for 3 minutes or until browned. Remove from pan (leave drippings in pan). Add onion, bell pepper, and celery to pan; sauté 4 minutes. Add garlic, thyme, and red pepper; sauté 4 minutes or until onion is tender and garlic is fragrant. Remove from pan.
Add remaining oil to pan. Add flour to pan, stirring constantly with a whisk. Cook 10 minutes or until roux is light brown, stirring constantly with a whisk. Gradually add broth, stirring constantly with a whisk. Add chicken and sausage, onion mixture, tomatoes, okra, and bay leaves; bring to a boil. Cover, reduce heat, and simmer 45 minutes, stirring occasionally.
Stir in parsley and shrimp; cook 5 minutes or until shrimp are done. Discard bay leaves. Serve over rice.