In a deep skillet, preheat 1 inch deep of oil to 350 degrees, set over medium heat. Or you can also test if the oil is ready for frying the flautas, by dipping a flauta or tortilla to see if the oil actively bubbles around it.
Place a comal or a dry skillet over medium heat until hot, then heat the tortillas on the comal for about 30 seconds per side; this will prevent them from breaking when rolling them into flautas.
Place 1 to 2 tablespoons of shredded chicken on each tortilla and roll them tightly. They should be thin, not chubby rolls. You can insert wooden toothpicks through 2 to 3 flautas at a time, so they will fry evenly and hold their shape.
Once the oil is hot, gently dip the flautas in it. Fry them until they have crisped and turned golden, about 2 to 3 minutes. Flip them over so they will brown evenly, for another minute. Remove the flautas from the oil and put them on a plate or tray lined with paper towels.
Alternatively, you may want to toast the flautas on a comal or bake in the oven lightly brushed with oil at 375, for 15 to 20 minutes.
Arrange them on a serving platter and garnish with lettuce, cheese, Mexican cream and salsa, or let your guests tailor to their taste.