In a large bowl, mix the taco seasoning with the chicken, tossing until the chicken is evenly coated. Add in the cheese and green chiles, stirring to combine.

Take one tortilla at a time and place about ⅓ cup of the chicken mixture in the center. Use your fingers to press the filling into a compact line across the middle. Roll the tortilla snugly around the filling, then secure it with a toothpick by weaving it through the overlapping edges, parallel to the roll. Repeat with the remaining tortillas and chicken mixture.

Preheat your oven to 250°F. In a large cast iron skillet, heat about ½ inch of oil over medium heat until it reaches 375°F. Fry four flautas at a time, turning them occasionally, until they are golden brown on all sides, which should take about 1 to 2 minutes. Transfer them to a paper towel-lined baking sheet and keep warm in the oven. Repeat the frying process until all the flautas are cooked. Serve them hot with sour cream.