Preheat the oven to 350 degrees F (175 degrees C).
Mix cream cheese, pepper Jack cheese, and taco seasoning in a medium-sized bowl. Fold in cooked shredded chicken. Divide mixture evenly onto 8 tortilla shells. Fold tortillas by tucking in sides first and then rolling. Place filled tortillas into a 9x13-inch baking dish with seam-sides down. Spray tops with cooking spray.
Bake in the preheated oven for 15 minutes. Turn chimichangas over and bake 15 minutes more.
Serve topped with Cheddar cheese, salsa, and sour cream.