Pound chicken between 2 sheets of plastic wrap to 1/4" thick; season with salt and pepper. Heat 1 Tbsp. oil in large skillet over high. Carefully place 1 chicken breast in skillet (laying it away from you) and cook until golden brown and nearly cooked through, about 3 minutes. Turn and cook until cooked through, about 1 minute (second side will not brown). Transfer to a large plate. Repeat with 1 Tbsp. oil and remaining cutlet. Let the cutlets rest while you make the slaw. Toss cabbage, onion, and red pepper flakes in a medium bowl; season with salt. Drizzle in vinegar and remaining 3 Tbsp. oil and toss again. Top cutlets with slaw.