Pat the chicken breasts dry, season generously with kosher salt and freshly ground black pepper, and lightly coat them in 1/4 cup of the flour, tapping off any excess.
In a large heavy pot, heat 3 tablespoons of the vegetable oil over medium-high to high heat until shimmering. Add the chicken and brown on both sides, about 8 minutes total. Remove the chicken to a plate and set aside.
Reduce the heat to medium-high. Add the sliced celery, diced onions, and diced bell peppers to the same pot (use any browned bits left in the pot). Cook, stirring occasionally, until the vegetables are softened, about 6–10 minutes. Remove the vegetables and set aside.
Wipe the pot if there is an excessive burnt residue, then add 3/4 cup vegetable oil and warm it over medium heat for a few minutes.
Gradually add the remaining 3/4 cup of flour to the warmed oil, stirring constantly with a wooden spoon or heatproof spatula. Cook the roux, stirring and scraping the bottom and sides of the pot to prevent scorching, until it reaches a deep mahogany brown color, about 10–20 minutes. Reduce the heat if it is browning too quickly. If the roux scorches, discard and start over.
When the roux is a deep mahogany brown, return the cooked vegetables to the pot. Add the minced garlic, cayenne pepper (start with 1/2 teaspoon and increase to taste), oregano, basil, thyme, and the bay leaves. Stir and cook together for about 3 minutes. Season lightly with kosher salt and black pepper.
Slowly pour in the 8 cups of chicken broth while stirring constantly to blend the roux with the liquid and prevent lumps. Continue stirring until the mixture is smooth.
Add the browned chicken breasts and the sliced, quartered andouille sausage to the pot. Bring the mixture to a gentle simmer. Skim off any excess fat or foam from the surface with a spoon.
Simmer the gumbo uncovered, maintaining a gentle simmer and occasionally skimming fat, until the chicken is falling off the bone, about 1 to 1 1/2 hours.
Remove the chicken and any bones from the pot. Discard the bones and shred or cut the chicken into bite-sized pieces. Return the chicken pieces to the gumbo.
Bring the gumbo briefly to a boil, then whisk in the 1 tablespoon filé powder (or gumbo seasoning with filé) a little at a time so it dissolves and does not clump. Taste and adjust seasoning with additional kosher salt and black pepper as needed.
To serve, spoon cooked white rice into bowls and ladle the gumbo over the rice.