Peel and devein the shrimp and place in the refrigerator. Place shrimp heads and shells in a large pot, and cover with 2 quarts of water. Cover, and simmer over medium-low heat until liquid is reduced by half. Strain out and discard shrimp heads and shells. Reserve shrimp broth.
Heat oil in a very large stockpot over medium-high heat. Stir in flour with a long-handled spoon. Cook and stir for several minutes until dark brown and flour is puffing and absorbing the oil. Slowly stir in chicken broth and an equal amount of water. Place chicken in the pot. Add onions, celery, bell pepper, tomatoes, garlic, bay leaves, red pepper flakes, Old Bay seasoning, and salt.Boil until chicken is no longer pink and the juices run clear, about 1 1/2 hours.
Remove chicken from the pot, and set aside until cool enough to handle. Remove and discard bones, and chop chicken into 1 inch pieces.
Return chicken back to the pot, along with reserved shrimp broth, crab meat, sausage, and shrimp. Add the file powder, and stir from the bottom of the pot. When the gumbo comes to a boil, remove from heat. Continue to stir from the bottom for 1 minute.Serve.
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