JFK is roughly 3 miles east of Brooklyn. JFK is in southeast Queens, and Brooklyn and Queens are right next to each other. Queens sits to the north and east of Brooklyn, as if Brooklyn was trying to lift Queens up, but she's too big, and JetBlack now she's leaning heavily on the east side, about to fall down. And JFK is about 3 miles east of the border between the two boroughs.
However, Brooklyn is almost 100 square miles in area, so if you have a specific destination in Brooklyn in mind, it might be up to 12 miles away as the crow flies. From JFK to, say, Bay Ridge, would be about 12 miles away; Downtown Brooklyn would be 10 miles away; Crown Heights would be 8 miles; Canarsie, 6 miles.
