In a large mixing bowl, combine the shredded cooked chicken, softened cream cheese, salsa, shredded Monterey Jack cheese, chili powder, cumin, garlic powder, onion powder, salt, and black pepper. Mix thoroughly until all ingredients are well combined and the chicken is evenly coated.

To prevent tortillas from cracking when rolling, warm them. You can do this in batches of 4-6 by wrapping them in a damp paper towel and microwaving for 30-60 seconds, or by quickly heating them on a dry skillet for 10-15 seconds per side until pliable. Keep them covered to retain warmth and moisture.

Take one warmed tortilla. Place about 2-3 tablespoons of the chicken filling in a line across the center, closer to one edge. Tightly roll the tortilla, starting from the edge closest to the filling, creating a taquito shape. Place seam-side down on a plate. Repeat with the remaining tortillas and filling.

Preheat your air fryer to 375°F (190°C). Lightly brush or spray the assembled taquitos with olive oil. Place taquitos in a single layer in the air fryer basket, ensuring they don't touch each other (cook in batches if necessary). Air fry for 8-12 minutes, flipping halfway through, until golden brown and crispy. Cooking time may vary based on your air fryer model.

Preheat oven to 400°F (200°C). Line a baking sheet with parchment paper. Lightly brush or spray the assembled taquitos with olive oil. Arrange them seam-side down on the prepared baking sheet. Bake for 15-20 minutes, or until golden brown and crispy, flipping halfway through.

Carefully remove the taquitos from the air fryer or oven. Serve immediately with your favorite dipping sauces like sour cream, guacamole, or extra salsa.