In a large mixing bowl, combine the shredded chicken, softened cream cheese, canned green chiles, chipotle sauce, salt, chili powder, ground cumin, smoked paprika, and garlic powder until smooth and fully incorporated.
Warm the corn tortillas by placing them on a microwave-safe plate and covering with a towel; microwave for 30 seconds and heat an additional 10–15 seconds if needed so they are pliable.
Preheat the air fryer to 400°F (204°C).
Spoon about 2–3 tablespoons of the chicken mixture along one edge of a warm tortilla, then sprinkle a heaping tablespoon each of the shredded Mexican blend and pepper jack cheeses over the filling. Roll the tortilla tightly and place seam-side down.
Arrange rolled taquitos in a single layer in the air fryer basket without touching; work in batches if necessary. Lightly spray the tops with cooking spray.
Air fry for 5 minutes, then flip each taquito, spray again, and air fry for an additional 2–4 minutes until crispy and golden.
Remove taquitos from the air fryer and repeat with any remaining rolled tortillas.
Serve immediately with guacamole, queso fresco, salsa, Mexican crema, pico de gallo, and chopped cilantro as desired.