One way to analyze has the logic as follows:
Sunset was 2030 in NYC on June 16, 2012
Disembarking from the plane and getting though customs was at least 30 minutes (and probably more)
Distance to Coney Island indicate it should take about 15 minutes
Finding and interpreting the postcard appeared to take 15 to 30 minutes
the 7 mile trip to Brooklyn Navy Yard on a Saturday would take about 30 minutes
safety setup for the ROADBLOCK was the major time here, probably about 15 minutes
taxi to Lombardi's Pizza took about 15 minutes
Pizza Delivery took at least 30 minutes
taxi to United Nations Building took about 15 minutes
final ROADBLOCK at UN took at least 2.5 hours, slightly more for Josh/Brent and more for Jaymes/James and Trey/Lexi.
That totals 5.25 hours, which makes the AA flight possible although AF22 has provides a great deal more buffer time.