The phrase to be spoiling for a fight is an idiomatic expression in English which means:
to be very eager to fight or argue
Therefore, she is not spoiling for a fight means she is not eager to fight or argue. In the context of the sentence:
She is baited to have a fight, but she is not spoiling for it.
it means that even though people are tempting her to have a fight or the circumstances of the situation are such that she is forced to have a fight (it can be a physical as well as verbal one), she doesn't really want to.