Heat a large Dutch oven or soup pot over medium heat. Add bacon then brown and remove to a paper towel-lined plate to drain. Reserve bacon fat in the pot, adding extra extra virgin olive oil if necessary to have 2 Tablespoons fat in the pot total.
Add the onions, bell peppers, and celery to the pot then season with salt and pepper and saute until softened, 8-10 minutes. Season the chicken with salt and pepper then add to the pot with the Cajun seasoning and saute for 5 minutes. Add garlic then cook for 1 minute, stirring constantly.
Sprinkle flour over the vegetables and chicken then stir to combine and cook while stirring constantly until the flour turns golden brown, 3 minutes. Slowly stream in the chicken broth while stirring and scraping up any brown bits from the bottom of the pot. Add the crushed tomatoes, water, bay leaves, red chili pepper flakes, and salt then turn the heat up to high to bring the soup to a simmer.
Once simmering, add the rice then stir to combine and cover the pot with a lid. Turn the heat down to low and simmer, stirring occasionally, for 15-20 minutes or until rice is just barely tender (it will continue to cook and soften in the hot soup.) Add cooked bacon back into the soup then let it sit and thicken off the heat for 10 minutes. Remove bay leaves and serve.