As long as flight isn't departing from horrible T4 TSA you are good.
As others say get in cab - you can take Trib/RFK Bridge if 90s+ upper and let him fight it via highway or take the QB Bridge if 80s down and ask him to take Queens Blvd directly to Woodhaven. It is all local but lights should be sequence and get you there within 40 mins. of exiting the bridge.
BTW - If driver takes Woodhaven ask him NOT to turn on to the Belt Pkwy but instead continue onwards and turn on the Conduit to get to JFK.