For time-savings, use precooked, diced rotisserie chicken in place of raw chicken.
Mix the chicken, cheese and taco sauce in a medium bowl. Set aside.
Pour 1/4 inch of oil in small to a medium nonstick skillet. Heat the skillet over medium heat until the oil ripples. Dip each tortilla in the oil about 2 seconds, turning once. Drain on a paper towel.
Spoon a rounded tablespoon or the mixture across the center of each tortilla. Roll up tightly.
Fry 3 or 4 flautas at a time in the hot oil, seam side down, for about 1 minute, turning once, until golden brown and crisp. Drain on paper towels. Continue until all of the flautas are cooked and crisp.
Mix the sour cream, oregano and garlic powder in a small bowl and stir to thin. Drizzle the sour cream sauce over the flautas. Serve the remaining sauce as a dip.