In a large bowl, combine the shredded chicken, shredded cheddar cheese, diced 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 microwave or on a skillet for about 20 seconds each to make them pliable and easier to roll.
Place about 2 tablespoons of the chicken mixture onto the lower third of each tortilla. Roll the tortilla tightly around the filling and secure with a toothpick if needed.
In a large skillet, heat about 1 inch of vegetable oil over medium-high heat until it reaches 350°F (175°C) or until a small piece of tortilla sizzles immediately when placed in the oil.
Carefully place the rolled flautas seam side down into the hot oil. Fry in batches, turning occasionally, until all sides are golden brown and crispy, about 3 to 4 minutes per batch.
Using tongs, 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, guacamole, and salsa on the side.