Prepare the chicken by boiling, baking, or grilling it. Shred into bite-sized pieces.
In a large mixing bowl, combine shredded chicken with sour cream, cream of chicken soup, and half a cup of Monterey Jack cheese. Add garlic powder, onion powder, cumin, salt, and black pepper. Mix until well combined.
Warm the flour tortillas in the microwave for about 30 seconds. Spoon about 1/4 cup of the chicken mixture onto each tortilla, roll them up tightly, and place seam-side down in a greased baking dish.
Mix the remaining Monterey Jack cheese with the cheddar cheese. Sprinkle half of this cheese mixture over the rolled tortillas. Pour any leftover chicken mixture over the top and sprinkle the remaining cheese on top. Bake in a preheated oven at 350°F for 25-30 minutes.
Let the enchiladas cool for about 5 minutes before serving.