Preheat the air fryer to 400 degrees F.
In a small bowl, whisk together eggs and milk to create an egg wash and set aside. In a separate shallow dish or plate, whisk together the flour, ground red cayenne pepper, salt, and black pepper, and set aside.
Working in batches, coat the chicken in the egg wash, then allow excess egg wash to drip off before transferring the chicken to the seasoned flour. Coat the chicken evenly in flour, then shake off any excess flour before transferring the chicken to the air fryer.
Once the air fryer is filled with a single layer of chicken, cook for 5 to 6 minutes. Flip, then cook for another 5 to 6 minutes, then transfer the cooked chicken to a large bowl. Continue dredging and air frying the chicken in batches until it's all cooked.
In the meantime, make the buffalo sauce. Combine melted butter, Frank's Red Hot, and ranch dressing in a small bowl and whisk until thoroughly combined. You may need to microwave the mixture for 15 to 30 seconds to help it combine evenly.
Finally, once all the chicken is cooked, toss it in the buffalo sauce until well-coated and set aside.