Brats are submissives who feel they are more entitled than they could ever possibly be as subs, in many cases they expect a potential Dom to show off or act up in order to prove their dominance instead of having a mature interaction. The whole concept of a brat really doesn't fly in most scenes because it is a clear implication of not really putting in real emotion or honest communication.
Within the BDSM lifestyle, the term brat is usually applied to a person of a submissive nature who acts up or causes trouble in order to attract attention. This is generally frowned upon as it is classed as topping from the bottom and trying to control the situation. "That submissive of mine was being a right brat this morning, trying to get me to beat her, so I sent her home and I'm not going to talk to her for a week."