A reference to the movie Office Space. Fifteen pieces of flair refers to doing the bare minimum amount of work required for any task. Barely meeting a standard, usually intentionally.
Courtney knew she was about to graduate and that her presentation wouldn’t affect her grades, so she went all 15 pieces of flair just to meet the requirement.
Drinking a large quantity of hard liquor in such a short time that you instantly go from sober to on the floor. This refers to the wrestler Ric Flair and his act of acting normal after taking a beating, only to suddenly fall flat on his face.