1. Combine water and chicken in a large pot; bring to a boil.
2. Reduce heat and simmer until chicken is tender, about 1 hour.
3. Transfer chicken to a strainer and cool; save cooking liquid; remove chicken from bones when cool.
4. Stir flour and oil in a heavy Dutch oven over medium heat.
5. Add 4 cups reserved chicken cooking broth, andouille, tomatoes with juice, pepper, celery, garlic, bay leaf, salt, thyme, basil, cayenne, and pepper; cover and simmer until thickened, about 1 1/2 hours.
6. Spoon off fat from surface; add chicken and file powder and simmer gently 15 minutes.
7. Serve over hot cooked rice.