If we take the Dune Encyclopedia as our guide, the very simple answer is that the KH was predicted rather than prophesied. The BG anticipated that a male who could access both male and female memories would be as powerful as they were, but without the flaws caused by their own lack of ability to access the other memories. This means perfect perception of the future, versus their own imperfect vision, perfect control of thier actions, versus their own imperfect control, etc.
The quest for the Kwisatz Haderach may have been the longest single-minded project in human history. The Bene Gesserit appears to have been the oldest continuous purposeful organization, and its purpose was to create a "human" who could tap both female and male reservoirs of ancestral memory. At some point along the millennia of Bene Gesserit history, their breeding program focused on power. Thereafter they sought the perfect human, total male as well as total female, in order to control events and impose the Bene Gesserit version of destiny on humankind. The Kwisatz Haderach, who was for ages a goal sought for his own sake, became a means to a narrower end.
The Bene Gesserit records are not entirely clear about just how this was to be achieved. The assumptions appear to have been so basic and to have evolved so gradually that they were never laid out in explicit, declarative form. From the events in the histories, however, and by interpolation and inference from records in the Rakis Hoard, we have pieced together a plausible rationale. Put simplistically, the Bene Gesserit came to believe that perfect memory would provide total predictability. Because the Bene Gesserit preserved the belief in a single creator of the universe, and believed that only this Being knew the temporal design of events all the way to their "end," they thought that to be able to predict the future was to possess the power of the creator.