Eobard Thawne: They're motivated by greed. They lack the commitment, the absolute focus.
The Flash: To kill me.
Eobard Thawne: Erase you.
Pastor: And we may never know exactly what happened... A break-in gone wrong, a disturbed mind. But we do know that this was a crime and a tragedy. And as we commit Nora to the care of our Lord, we know her son, Barry, will need all our prayers and help to see him through this terrible loss.
Thomas Wayne: Hologram party. Ingenious. Saves a fortune on snacks.
Thomas Wayne: Not what you were expecting?
Barry Allen: No, Thawne.
Thomas Wayne: Who?
Barry Allen: My opposite, the Reverse Flash. Eobard Thawne.
Thomas Wayne: What kind of name is Eobard?
Barry Allen: The 25th century kind.
Answer: Flash couldn't travel through time later in the movie not because Zoom was alive but because Zoom was also tapping into the Speed Force, preventing Flash from gathering enough of the Speed Force to break the Time Barrier. When Flash originally went back in time it's likely because Zoom was in custody, therefore not tapping into the Speed Force at that time.