Preheat the air fryer to 400 degrees F (200 degrees C).
Working with one tortilla at a time, place 2 tablespoons of shredded chicken on one end of the tortilla. Place 1 tablespoon shredded cheese on top of the chicken. Roll to form the taquito, starting at the filled side. Use 2 toothpicks to secure the taquito along the seam. Repeat with remaining ingredients.
Open up the air fryer and spray the basket with cooking spray. Place 4 taquitos (toothpicks will be facing up) into the basket, making sure they're not touching, and spray the tops with more cooking spray.
Air-fry until the taquitos are brown and crispy to your liking, 5 to 6 minutes. Repeat with remaining taquitos. Remove toothpicks before serving.