Preheat air fryer to 400°. Pulse torn bagel in a food processor until coarse crumbs form. Place 1/2 cup bagel crumbs in a shallow bowl; toss with panko, cheese and pepper flakes. (Discard or save remaining bagel crumbs for another use.)
In a microwave-safe shallow bowl, microwave butter until melted. Sprinkle chicken with salt. Dip in warm butter, then coat with crumb mixture, patting to help adhere. In batches, place chicken in a single layer on greased tray in air-fryer basket.
Cook 7 minutes; turn chicken. Continue cooking until coating is golden brown and chicken is no longer pink, 7-8 minutes. Serve immediately.