what incentive, other than the law, does an Atheist have to be moral, let alone to teach it?
Since you see fit to ask the question, I feel certain that you would be surprised to learn the answer.
If anything, disbelief in a God (particularly one of the Abrahamic mold) is a bonus for understanding and practicing morality.
Our incentive is actually the very same that one would expect, and that most if not all Christians and Muslims have as well: it is simply a good idea to be moral. It makes life easier and more joyful.
Do you think that theists are any different in this regard?To advise people on it? Besides, I've yet to meet a group of Atheists who agree on any given set of morals, since most think morality isn't any sort of an absolute. For them, it's up for discussion and "reform".