The visitors stunned the home side with two goals inside the opening 12 minutes. First Jay Emmanuel-Thomas picked out the Sam unmarked Baldock wide on the right who then raced into the box unchallenged to send a superb drive into the net after just three minutes.
Then a corner from the left delivered by Tyrone Barnett was met by Marlon Pack who angled his header into the corner of the net.
The home side failed to make any impression although they were given hope in the 44th minute when City keeper Simon Moore spilled a shot from Dean Cox leaving Kevin Lisbie with a simple tap-in.
Orient did improve after the interval and Moses Odubajo, Lisbie and David Mooney all came close to finding the equaliser but there hopes were ended with 15 minutes remaining.
Orient keeper Shawan Jalal, who had looked unsafe all evening, failed to cut out a cross by Greg Cunningham to present Flint with a simple headed goal from 10 yards to restore City’s two-goal cushion and earn a memorable victory.