JFK Airport advice please

You could take LIRR from Flatbush & Atlantic out to Jamaica, then take the AirTrain to JFK. But you're humping a lot of baggage.

Best way out of the Slope/PH in a cab or car service - insist on it:
Eastern Parkway out to Atlantic Ave.
Make right onto Atlantic.
Go a couple miles East.
Make right onto Conduit Blvd.
You'll be at JFK quicker than a flash.
Follow directions in a reverse manner to get home, except the left off Atlantic will not be on Eastern Parkway, it will be at the next legal left turn, [street name escapes me now] which has a left-hand turn lane.
That street goes south to Eastern Pkwy, then you make a right.
DONT LET CABBIES TAKE YOU VIA THE BELT OR BQE OR EVEN WORSE THE VAN WYCK.

Yes, use Eastern and call them for a pick up when you return too. The Yellow cabs won't know how to get back

If you use that route from JFK you can take a yellow cab to return home..it is pretty cheap because that route takes you to PS so quickly..also coming back from La Guardia take the Belt to the Kent Ave. exit and then go straight until you make a left on Vanderbilt...it is really fast also...

sorry you are right the BQE thanks