How to Make Air Fryer Greek Chicken. This chicken is cooked quickly (about 13 minutes) and it's packed full of flavour. Keep a close eye on the chicken while it's cooking. Check 2 or 3 times during cooking, and give the air fryer basket a shake to ensure the chicken cooks evenly and is browned all over. My favourite way to serve this chicken is piled on top of warmed flatbreads or pita, with lettuce, tomatoes and a drizzle of oil.