Combine the chicken rice, beans, enchilada sauce, green chilies, cilantro, lime juice, cumin, oregano, chile powder, garlic powder, salt, and pepper together in a bowl.
Lay out the tortillas, layer about 1/4 cup cheese then 1/2 cup of the filling in the center of each tortilla.
Fold one side of the tortilla over the filling, followed by the other side (so that the tortilla is folded into thirds). Press lightly to flatten. It should be thick and flat, not rounded like a burrito.
Spray the air fryer basket. Place the wraps in the air fryer basket. Use toothpicks or rack to keep the tortilla from flying open if needed. Spray the tops and cook for 5-6 min at 350 °F.
Serve warm with sour cream, salsa, or other toppings of your choice!