They used to hand out fast track immigration cards on board in business but I haven't noticed them on my last few flights (I don't need one so may not have been paying enough attention). You might have to ask the crew for one. I don't know if a J boarding pass is sufficient I'm afraid.
Alternatively you can book one of the DXB meet and greet services if you know you'll be arriving at a peak time. The have their own immigration channel even for the basic service.