Add the oil, chicken and sausage rounds to a stockpot on medium-high heat. Sear the chicken to get color and sausage to get color and render fat, but not to cook fully. As the parts finish searing, use a slotted spoon to remove them and place on a plate, leaving the fat in the pot, about 10 minutes total.
Add the butter, flour and Cajun seasoning to the pot. Cook on medium heat, constantly stirring, until the roux becomes a rich, dark caramel color, 10 to 15 minutes.
Add the bell peppers, onions, celery, jalapenos and garlic. Season with salt and pepper. Cook, stirring, to coat, until everything gets tender, 5 to 8 minutes, then add the stock base and 8 cups water and stir to mix the base into the pot. Add the bay leaves and cover the pot to simmer until the gumbo is thickened, 30 minutes to 1 hour.
Add the reserved chicken and sausage, then stir in the file powder. Simmer, uncovered, for another 30 minutes.
Shred the chicken in the pot. Serve over rice with a shake of hot sauce and file powder.