In a large bowl, combine the shredded chicken, shredded cheddar cheese, chopped onion, chopped cilantro, ground cumin, chili powder, garlic powder, salt, and black pepper. Mix well until all ingredients are evenly incorporated.
Warm the corn tortillas in a dry skillet over medium heat for about 20 seconds on each side to make them pliable. Keep them warm wrapped in a clean kitchen towel.
Place about 2 tablespoons of the chicken mixture onto the lower third of each tortilla. Roll the tortilla tightly around the filling to form a flauta. Secure with a toothpick if necessary.
Heat about 1 inch of vegetable oil in a large skillet over medium-high heat until it reaches 350°F (175°C).
Carefully place the flautas seam side down in the hot oil, cooking in batches if needed. Fry for about 2 to 3 minutes on each side or until golden brown and crispy.
Use tongs to transfer the cooked flautas to a paper towel-lined plate to drain excess oil.
Remove toothpicks before serving. Serve the chicken flautas hot with sour cream and salsa on the side.