Preheat the oven to 375 degrees F.
To a mixing bowl add the shredded chicken, 2 ounces of the Monterey Jack cheese, 2 ounces of the blue cheese, and the sliced celery.
Stir together the enchilada sauce and hot sauce or wing sauce. Adjust the spiciness to your liking to adding more sauce if you’d like. Add 3/4 cup of the sauce to the chicken/cheese filling and stir until combined. Spread 1/4 cup of the sauce on the bottom of a 13-by-9-inch baking dish.
Gently warm the tortillas either in a microwave covered by a damp paper towel or individually in a dry skillet over medium-heat to make them soft and pliable (otherwise they will crack and break as you roll them). While each tortilla is still warm, fill it with several tablespoons of filling and roll it tightly closed. Place seam-side down in the prepared baking dish. Repeat with the remaining tortillas and filling.
Spread the remaining sauce over the enchiladas and top with the reserved Monterey Jack cheese. Bake for about 20 to 25 minutes or until bubbly and hot and the cheese has melted. During the last couple minutes of baking, add the remaining ounce of blue cheese to the top of the enchiladas and return them to the oven until just melted. Top with the sliced scallions and serve immediately.