I feel like this was recently posted but I'll answer again...

AF is in Terminal 1. DL operates from T2/T3/T4. Upon arrival to JFK on DL, you'll have to head to the AirTrain. Exit the terminal and get on the "All Terminals" train (the inner loop of the train). The AirTrain will take you to T1 where you'll have to go through security again.

http://www.panynj.gov/airtrain/around_jfk.html