What is Professor Zoom's role in the Flashpoint Paradox?

Professor Zoom taunting The Flash over the death of the hero's mother is responsible for the timeline change. In the end, it is revealed that The Flash is responsible for the creation of the alternate world because, after Zoom's taunting, he traveled back in time to save his mother. This created a chain of events which led the world to a destructive situation. Professor Zoom took advantage of this situation.

Many things are implied with the film and require some knowledge of the comics. Usually, films set-up the background within themselves; instead, this film makes some very minor assumptions on the part of the audience.

As a time-traveling speedster, Professor Zoom is immune to the changes in the timestream in the same way Barry Allen was (for as long as he could hold out; we witness him eventually merge with his alternate universe memory history). Professor Zoom, at any point, could have traveled back to the past to observe Barry stopping the crime which killed his mother, in order to gain knowledge of how that incident changed the timeline.

Professor Zoom's motivation is to torture Barry Allen. He lets Barry know that by altering history to save one life, Barry caused the chain of Flashpoint events that put the world on the brink of destruction. Zoom took no part in this other than to be an observer, and to taunt Barry.