A FlyerTalk Posting Legend
Join Date: Sep 2009
Location: Minneapolis: DL DM charter 2.3MM
Programs: A3*Gold, SPG Plat, HyattDiamond, MarriottPP, LHW exAccess, ICI, Raffles Amb, NW PE MM, TWA Gold MM
Posts: 100,417
DL is sometimes willing to check bags through on separate tickets/PNRs and DL does interline with SQ, but this is less likely since DL and SQ belong to different alliances.
The best chance is to being printouts of your SQ itinerary and ticket receipt (showing the ticket number) to the airport and ask nicely when you check the bags for your DL flight.
If your flight lands at T4, note that SQ uses a separate wing of this terminal but it's all the same building. From T2, DL runs an airside free bus (called the JFK Jitney--you are not required to show your boarding pass but employees sometimes try to ask) to T4, but this won't help if you must claim a checked bag at T2.