Preheat the oven to 200°F and set a wire rack inside a baking dish to keep cooked flautas warm.
In a medium bowl, combine 3 cups shredded chicken, 1 cup shredded Monterey Jack, 1/2 cup salsa, 1/4 cup sour cream, 1 (4-ounce) can diced green chiles, and 1 teaspoon chili seasoning; season with Kosher salt and ground black pepper to taste.
Lay a tortilla flat and place about 3 tablespoons of the chicken mixture in the center. Roll tightly and secure with a toothpick; repeat with remaining tortillas and filling.
Pour oil into a large, deep saucepan to a depth of about 3/4 inch and heat over medium until it reaches 375°F.
Fry 2 to 4 flautas at a time using tongs, turning as needed, 2 to 4 minutes until evenly golden brown. Adjust heat to keep the oil temperature steady.
Transfer fried flautas to a paper towel–lined plate to drain and season immediately with a little salt. Then move them to the prepared wire rack in the warm oven while you fry the rest.
Remove toothpicks and serve the flautas warm with your choice of toppings.
