Place chicken in a 6- to 8-quart stockpot and pour in enough water to completely cover the chicken; bring to a boil, reduce heat to medium, and simmer until chicken is no longer pink at the bone and juices run clear, about 1 hour. An instant-read thermometer inserted into the thickest part of the thigh, near the bone should read 165 degrees F (74 degrees C).
Remove chicken from water and place on a work surface to cool, retaining the resulting chicken stock in the stockpot.
Cook and stir millet flour and vegetable oil together in a large frying pan or skillet over medium heat until roux is smooth and slightly darker than peanut butter, about 10 minutes.
Mix onion, green bell pepper, and garlic into roux; cook and stir over low heat until fragrant, 2 to 3 minutes. Transfer onion-roux mixture to stockpot with chicken stock.
Bring chicken stock mixture to a simmer over medium heat; add andouille sausage, celery, green onion, bay leaves, salt, thyme, and cayenne pepper and simmer for 1 hour.
Remove skin from cooked chicken and discard. Pull meat from the bones and chop into bite-size pieces; discard carcass. Add chicken meat to broth mixture and simmer until chicken is heated through, 5 to 10 minutes.
Remove stockpot from heat, stir file powder into gumbo, and remove and discard bay leaves.