Whisk together the salt, peppers, chili powder, and paprika in a large bowl. Add the chicken pieces and use your hands to toss until evenly coated; set aside.
Heat the oil in a large pot or Dutch oven over medium-high heat until it begins to smoke slightly. While the oil heats, toss the chicken with flour to coat.
Shaking off the excess flour from the chicken, transfer the pieces to the hot oil and fry until golden brown on all sides. Fry the chicken in two batches so you don't overcrowd the pan -- the chicken should be in one layer, and not on top of each other. Reserve the leftover flour. Use a slotted spoon to transfer the chicken to a deep plate, leaving the oil in the pan.
Add the remaining flour to the oil and cook (I added a little more oil and flour at this point, because the leftovers didn't seem like enough -- there should be at least 1/2 cup of each). Monitor the heat -- you don't want the flour to burn! -- and cook, stirring constantly, for 5 minutes to create a medium-brown, peanut butter-colored roux.
Add the onion, celery, poblano, and garlic and cook 5 minutes more. Add the chicken tomatoes, broth, thyme, bay leaves, and hot sauce. Simmer over low heat for 45 minutes, stirring occasionally, until thickened to a light gravy and the chicken is tender enough to shred with a fork. Taste and adjust seasonings, adding more salt or hot sauce as desired. Serve over rice, garnished with scallions.