Preheat your air fryer to 400°F (200°C) for about 5 minutes.
In a mixing bowl, combine the cooked shredded chicken, garlic powder, onion powder, paprika, salt, and pepper. Mix until well combined.
Lay out each flour tortilla on a flat surface. Place a slice of ham on each tortilla, followed by an equal portion of the chicken mixture, and finally top with shredded cheddar cheese.
Roll up each tortilla tightly, tucking in the sides as you go to secure the filling.
Lightly spray the wraps with cooking spray or drizzle with a small amount of olive oil to help them crisp up in the air fryer.
Place the wraps in the preheated air fryer basket, making sure they are spaced out so air can circulate freely. You may need to cook them in batches depending on the size of your air fryer.
Air fry for 6-8 minutes or until the wraps are golden brown and crispy. Use tongs to flip them halfway through for even cooking.
Carefully remove the wraps from the air fryer and let them cool for a minute before cutting them in half. Serve warm.