In a large mixing bowl, combine the shredded chicken, cream cheese, cheddar cheese, diced jalapeños, garlic powder, onion 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, folding in the sides as you go to create a taquito.
Heat about 1 inch of cooking oil in a large skillet over medium heat.
Once the oil is hot, carefully add the taquitos, seam side down, in batches. Fry until golden brown and crispy, about 3-4 minutes per side.
Remove the taquitos from the oil and place them on a paper towel-lined plate to drain excess oil.
Serve warm with sour cream and salsa on the side.