Any time I fly from the US I cannot get a mobile BP from EK. have to see an agent either in an EK lounge or at check in.
What terminal are you arriving at JFK? If T4, then you can just stay airside and get your BP from the lounge (when it opens). You have not needed to show BP at TSA for a long time in most cases, BUT that being said I think in order for the ID system to work you need to be checked into your flight, which I am not sure you actually would be yet without them issuing a BP for your EK flight.
Ty, I'm at JFK now on the TWA hotel rooftop to watch the eclipse. Going to head over to T4 after. I came into T8. I am checked in for certain, just no BP without a person to issue. Hopefully by 4 or 430 someone will be around soon.