Place beaten egg in a shallow bowl, add flour to another bowl. Combine bread crumbs, Parmesan cheese, flax seed meal, lemon zest, oregano, cayenne, salt, and pepper in a third bowl.
Dip each chicken breast into flour, then egg, and lastly bread crumb mixture, fully coating the chicken on both sides. Set coated chicken breasts into an air fryer basket. Depending on the size of your air fryer, you might need to cook them in batches.
Set the air fryer to 375 degrees F (190 degrees C). Cook chicken breasts for 10 minutes. Turn and cook until chicken is no longer pink in the center and the juices run clear, about 5 more minutes. The coating should be golden and an instant-read thermometer inserted into the center should read at least 165 degrees F (74 degrees C).