Bill the Lizard, a moderator on Chat, said that he can star his own messages. I don't think anyone should be allowed to star their own messages on Chat, even moderators. I don't see how it could be useful, so I think that this is a bug and should be removed.
Yea; it does seem like it should be.
I vote for the following image to pop up when someone tries to flag their own message:
Room owners can also star their messages, but the process of going about this actually appears as a legitimate bug and not an allowed power.