Flatten the chicken: pound the thicker end of each breast to an even 1/2-inch thickness, then cut each breast in half to make 4 pieces.
Make the marinade: whisk together the buttermilk and pickle juice in a bowl.
Marinate the chicken: add the chicken pieces to the buttermilk mixture, toss to coat, cover with plastic wrap, and refrigerate at least 6 hours or overnight.
Prepare dredging stations: in a shallow bowl combine the flour, garlic powder, paprika, 1/2 teaspoon kosher salt, and cayenne. In a second bowl whisk the beaten egg.
Coat the chicken: working one piece at a time, shake off excess marinade, dredge in the flour mixture, dip into the egg, then dredge again in the flour, pressing with the back of a fork so the coating adheres.
Rest and prepare air fryer: let the coated chicken rest 15 minutes (optional) to help the breading adhere. Line the air fryer basket with a parchment liner if using and preheat the air fryer to 380°F (if your model requires preheating).
Air fry the chicken: place coated pieces in the basket in a single layer (work in batches if needed), spray the tops lightly with olive oil spray, and cook at 380°F for 15 to 18 minutes, turning halfway, until golden and an instant-read thermometer reads 165°F.
Make the sriracha mayo: while the chicken cooks, whisk together the light mayo and sriracha in a small bowl.
Assemble sandwiches: spread sriracha mayo on the tops of the rolls, place a cooked chicken piece on each bottom roll, top with dill pickle chips, and finish with the roll tops.