Wrap the flour tortillas in a damp kitchen towel and place in the low oven until they warm through and become pliable.
Place a large skillet over medium-high heat; add 1 turn of the pan of EVOO, about 1 tablespoon, and the butter. Once the butter has melted and the pot is hot, add the ground chicken. Cook until brown, about 5-6 minutes, using the back of a wooden spoon to break the meat up into small pieces.
Add the carrot, onion, celery, garlic and some salt and pepper. Cook, stirring frequently, for about 3-4 minutes.
Add the chicken stock, scraping up any brown bits on the bottom of the pot. Add the hot sauce, black beans and the cilantro. Stir to combine and cook until the beans are heated through, a minute or two.
Remove the warm tortillas from the oven, place a few heaping spoonfuls of the buffalo chicken/black bean mixture on the bottom of a tortilla, but don't overfill it.
Top with some cheese, avocado and tomato. Roll the short end of the tortilla over the filling, fold in the other two sides and then continue to roll it up until you have a tight burrito package. Once you have finish rolling all the burritos, turn the oven up to broil. Place burritos in a shallow backing dish and sprinkle with remaining cheese, place under the broiler for 2-3 minutes to melt the cheese.