Preheat the oven to 425°F (220°C).
In a large bowl, combine the shredded chicken, cheddar cheese, Monterey Jack cheese, chopped onion, cilantro, ground cumin, chili powder, garlic powder, and salt. Mix well until all ingredients are evenly incorporated.
Warm the corn tortillas slightly to make them pliable by wrapping them in a damp paper towel and microwaving for 30 seconds.
Place about 2 tablespoons of the chicken mixture on one end of each tortilla and roll tightly to enclose the filling.
Place the rolled taquitos seam side down on a baking sheet lined with parchment paper.
Lightly spray the taquitos with cooking spray to help them crisp while baking.
Bake in the preheated oven for 20 to 25 minutes, or until the taquitos are golden brown and crispy.
Remove from the oven and let cool for 5 minutes before serving.