In a small bowl, mix together, the mayo, lime juice, salt, clove of garlic and mole paste. Using an immersion blender, blend until smooth. (Throw all the ingredients in the food processor if you don't have an immersion blender) set in the fridge.
Start by warming up a couple of tortillas, I like to work in batches of 5. (Pop them in the microwave for about 45 seconds. Stiff, cold tortillas will rip when they're rolled.)
Fill your tortilla with a spoonful of chicken, and a few strings of oaxacan cheese. Roll tortilla tightly
Add 1 tablespoon of vegetable oil to a medium sized frying pan and place your flautas seam down and fry each side for about a minute until golden brown.
Top with lettuce, drizzle on the aioli and finish garnishing with crumbled cotija.