Using the Jetblue App?
 

I just used my iPhone JetBlue app to check in and get my boarding pass. It also lets me have my boarding pass. But for the wife and kids who are already checked in, can I get their boarding passes on my phone app as well?

I don't think so. I'm pretty sure it is only one BP per device. You could theoretically save the JPG image from each of the three and bring them up one at a time at the gate but I'd think that's more work than just getting the piece of paper.