Place chicken in a large pot; add enough water to cover. Cover the pot and bring to a boil; reduce heat to medium-low and simmer until meat falls off the bone, about 90 minutes. Remove chicken, let cool, and shred meat; skim broth and reserve.

Melt butter in a large skillet over medium heat. Add onion, bell pepper, and celery; cook and stir until tender, about 5 minutes. Stir in garlic; cook until fragrant, about 1 minute. Add sausage, okra, diced tomatoes, corn, tomatoes with green chilies, cayenne pepper, salt, black pepper, and reserved broth; bring to a gentle boil over medium-high heat. Simmer until liquid is reduced by half, about 30 minutes.

Stir shredded chicken and shrimp into skillet; simmer until shrimp turns bright pink and okra tender, 5 to 7 minutes. Off heat, stir in file powder. Serve with rice.