Is it possible to put a vintage crankset on a modern bottom bracket, assuming both are JIS? My concern is that the most older crankset were designed for use with a fixing bolt that goes over spindle, but modern bottom brackets use crank bolts that screw into the spindle. Would this be a problem?

Are you referring to square taper axles... hollow vs. solid ?? Better quality axles tend to be hollow (lighter) and need a bolt, instead of a nut. I think the critical factor is axle length for the particular crankset.

Older BB's used bolts bolts that screwed into the spindle or nuts that screwed onto a threaded stud at the end of the spindle. The only thing that matters is that both are JIS and that the dimensions are proper. Modern cranksets typically use a shorter BB spindle, but various lengths are available.

As long as they both are JIS they should both fit; whether the end of the spindle is threaded for a nut or tapped for a bolt should not matter. However, as pointed out above, the spindle length needs to fit the crankset's requirements.

+1, most vintage bikes were fitted with longer Bottom bracket spindles, so make certain you have proper chain line after the cranks are fitted.
Regards