Cut each chicken breast in half at an angle to create 4 thinner pieces total. Place in a gallon-size resealable bag, along with pickle brine. Seal bag, pushing out excess air, and place in a bowl or dish. Refrigerate 1 hour.
Meanwhile, in a wide bowl, whisk the egg and milk. In another dish, combine the bread crumbs, onion powder, and black pepper. Season with salt.
Heat air fryer to 350°F. Spray basket with the cooking spray.
Dip each piece of chicken into egg mixture, discarding brine. Letting excess egg drip back into dish, transfer chicken to bread crumbs and press to coat. Repeat with remaining chicken.
Place chicken into air fryer in single layer. Spray tops with cooking spray. Cook 12 min., turning chicken over halfway through. Increase temperature to 400°F and cook 3–4 min., until golden brown.
Stir sauce ingredients together. Brush cut sides of the buns with the butter. Place chicken on the bun bottoms, along with sauce. Top with the pickles and bun tops. Serve immediately.