Place chicken in a large pot; add enough water to cover. Cover 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; cook and stir onions, bell pepper, and celery until tender, about 5 minutes. Stir in garlic and cook until fragrant, about 1 minute. Add diced tomatoes, tomatoes with green chilies, andouille sausage, okra, corn, salt, pepper, cayenne pepper, and reserved broth; bring to a gentle boil over medium-high heat. Simmer until liquid is reduced by half, about 30 minutes.
Mix shredded chicken and shrimp into skillet; simmer until shrimp turns bright pink and okra is tender, 5 to 7 minutes. Remove skillet from heat and stir in file powder. Serve with rice.
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