I have experienced menstrual synchronicity myself (with my sister, with my cohort in university, with co-workers), although I have no way of telling if it was coincidence or not. However, it occurs to me that evolution should kill menstrual synchronicity.
If every female in the group is menstruating at the same time, that means they're also all fertile at the same time. Which means that, outside of that one fertile window, any sex that is had in the entire group is wasted (from a survival-of-the-species point of view - qualify everything I say in this blog post with "from a survival-of-the-species point of view"). And if the male-female ratio is such that not all females can get all the sex necessary to become pregnant during the fertile window, a whole menstrual cycle is wasted.
But if there's a female who isn't synchronized with the rest of the group, she can get pregnant when no one else can. If males are at a premium (especially given the trends observed in our primate ancestor of females being more inclined to mate while fertile and males being more attracted to fertile females), she has her pick of all the males during her fertile window, as opposed to having to share with the rest of the group, thus increasing her chances of becoming pregnant
Even if there is no evolutionary disadvantage to synchronicity, it seems like there is a bit of an advantage to asynchronicity.
Of course, there's also the fact that, for most of evolutionary history, human and primate females spent most of their time either pregnant or lactating, and therefore unable to become pregnant anyway, which makes the impact of menstrual synchronicity or asynchronicity seem tiny. But, on the other hand, evolution has taken places over millions and millions of years. And millions and millions of tiny impacts can add up to something significant.