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 microwave wrapped in a damp paper towel for about 30 seconds to make them pliable.
Place about 2 tablespoons of the chicken mixture onto the center of each tortilla. Roll the tortilla tightly around the filling and secure with a toothpick if needed.
Pour vegetable oil into a large skillet to a depth of about 1 inch and heat over medium-high heat until the oil reaches 350°F (175°C) or a small piece of tortilla sizzles immediately when added.
Carefully place flautas seam side down into the hot oil, frying in batches to avoid overcrowding. Fry for 2 to 3 minutes on each side or until golden brown and crispy.
Use tongs to remove the flautas from the oil and drain on a paper towel-lined plate to remove excess oil.
Remove toothpicks before serving. Serve the chicken flautas hot with sour cream, guacamole, salsa, and lime wedges on the side.