Vale started the game as if they were going to prove too strong for the visitors as Sean Rigg and Marc Richards threatened in the opening two minutes.
But Barnet opened the scoring in the seventh minute, O'Flynn firing in from close range after Paul Furlong headed down a cross from Albert Adomah.
And the Bees remained a real threat on the break as O'Flynn and 41-year-old Furlong both went close to adding a second in the closing stages of the first half.
Despite some heavy Vale pressure after the break, O'Flynn sealed the visitors' win when he netted a well-placed shot from Albert Jarrett's cross six minutes from time.
Source: Team Talk
Source: Team Talk