That's a pretty tight connection with the need to claim and re-check baggage, especially because I'm guessing the BA check-in will close 60 minutes prior to scheduled departure. You'll probably make it but if anything goes wrong you're going to be on the hook for a change fee with BA.

JetBlue will not be able to interline bags for you.

Even without checked bags it is a bit of a risk because of the separate carriers and the need to be checked in 60+ minutes out, but not quite as bad.