In a mixing bowl, mix the taco seasoning with the shredded chicken until well coated. Stir in the shredded cheese and chopped green chiles.
Warm the tortillas in the microwave for 20-30 seconds wrapped in a damp paper towel until pliable. Spoon about 1/3 cup of the chicken mixture onto the center of each tortilla, press it into a line, and tightly roll.
Heat canola oil in a large skillet over medium-high heat until it reaches 375°F. Work in batches, frying the flautas until they are golden brown on all sides, about 1 to 2 minutes per batch.