By its nature The Flashpoint would have changed nearly everything. I imagine if The Reverse-Flash never killed Barry's Mother and spent the subsequent years in a cell then the Singularity that drew Zoom's attention to Earth-1 never occurs and Zoom's rampage on Earth-2 continues uninterrupted. I don't think it was ever clarified if he had access to other earth's but he did know of their existence, so perhaps his madness on Earth-2 carries on until he finally burns out... of course poor Jay Garrick will either be killed by the despairing Zoom or dies of starvation in the glass cage. Though on the other hand maybe Harrison Wells(2) is galvanised to develop the strategy that finally ends Zoom?
He did travel to other Earths thanks to the powerboost provided by the Velocity drug, hence him fighting Jay Garrick in the first place, but like you said, it was the Singularity which made him aware of Barry. Without knowing it would be sheer chance that Zoom would travel to Earth One given the infinite amounts of Parallel Universes.