In a large Dutch oven, combine the vegetable oil and gluten-free flour over medium heat. Stir constantly for about 30 minutes, or until the roux develops a deep brown color. Keep stirring and watch the heat closely. You don't want the roux to burn.
Add the diced onion, green bell pepper, and celery to the browned roux. Stir to combine and cook for about 5 minutes, until the vegetables begin to soften.
Gradually add the beef broth, a little at a time, stirring as you go to incorporate it into the roux. Add the water, beef bouillon, Worcestershire sauce, cayenne pepper, salt, dried thyme, and bay leaves.
Add the diced chicken thighs and sliced andouille sausage. Bring the gumbo to a boil, then reduce the heat and simmer for 1–2 hours, or until the chicken is fork tender.
Taste and adjust the seasoning as needed. Remove the bay leaves before serving.
Serve hot over cooked rice.