Peel shrimp; devein, if desired.
Sprinkle chicken evenly with salt, black pepper, and red pepper.
Heat oil in a Dutch oven over medium heat. Add chicken, and cook, stirring constantly, 8 to 10 minutes or until browned on all sides. Remove chicken using a slotted spoon.
Add ham to Dutch oven, and cook, stirring constantly, 5 minutes or until lightly browned. Remove ham using a slotted spoon.
Add garlic and next 3 ingredients to Dutch oven; stir to loosen particles from bottom. Stir in ham and chicken. Cover, reduce heat to low, and cook, stirring occasionally, 20 minutes.
Add chicken broth. Bring to a boil over medium-high heat; cover, reduce heat to low, and simmer 35 minutes. Add tomatoes and next 3 ingredients. Bring to a boil over medium-high heat; cover, reduce heat to medium-low, and simmer 20 minutes. Stir in shrimp and hot sauce; cook, covered, 10 more minutes or until liquid is absorbed and rice is tender.
Eula Mae's Cajun Kitchen: Cooking Through the Seasons on Avery Island