Put cayenne pepper sauce and oil in a large zip-top bag. Add cooked chicken, seal bag, and shake to coat chicken well. Refrigerate for 30 minutes to allow chicken to marinate.
Pour chicken and sauce in a microwave-safe dish, cover, and heat 2 minutes or until hot (or pour chicken and marinade in a pan and warm on the stove over medium heat).
Lay 4 flour tortillas on the counter. Spoon 1/4 of chicken in the center of each one. Drizzle with the warm marinade if you want to. Top each with 1/4 of the cheese and 1/4 of the lettuce. Drizzle each with 1/4 of the dressing.
Fold each taco in half, or roll it up. Slice in half if you want to.