Cut each chicken breast in half horizontally to create 4 thinner cutlets. Place each cutlet between plastic wrap and pound gently to an even 1/2-inch thickness. In a bowl, combine the buttermilk and hot sauce, then add the chicken cutlets. Cover and refrigerate for at least 1 hour, or up to overnight.
In a large shallow dish, whisk together the flour, cornstarch, garlic powder, smoked paprika, onion powder, salt, and black pepper.
Remove a chicken cutlet from the buttermilk, letting the excess drip off. Dredge it in the seasoned flour, pressing firmly so the coating sticks. Dip it back into the buttermilk briefly, then dredge in the flour once more for a thick, shaggy coating. Repeat with all cutlets.
Preheat the air fryer to 375°F for 3 minutes. Spray the basket generously with cooking spray.
Place 2 breaded chicken cutlets in the air fryer basket. Spray the tops generously with cooking spray. Air fry for 6 minutes, then carefully flip, spray the other side, and cook for 5 to 6 minutes more until deeply golden and the internal temperature reaches 165°F.
Repeat with the remaining 2 cutlets.
Toast the brioche buns lightly in the air fryer for 1 to 2 minutes. Spread mayonnaise on each bun, then layer with lettuce, tomato, the crispy chicken cutlet, and pickle slices. Serve immediately.