In a large mixing bowl, combine the shredded chicken, cheddar cheese, Monterey Jack cheese, cream cheese, cilantro, garlic powder, onion powder, chili powder, salt, and black pepper. Mix until well combined.
Warm the flour tortillas in a microwave for about 30 seconds to make them pliable.
Place about 2-3 tablespoons of the chicken mixture in the center of each tortilla. Roll tightly, tucking in the sides as you go to secure the filling.
Heat about 1 inch of vegetable oil in a large skillet over medium heat.
Once the oil is hot, carefully place 3-4 taquitos in the skillet, seam side down. Fry for about 3-4 minutes on each side, or until golden brown and crispy.
Remove the taquitos from the skillet and place them on a paper towel-lined plate to drain excess oil.
Repeat the frying process with the remaining taquitos.
Serve warm with sour cream and salsa on the side.