Since the introduction of ICS (ice cream sandwich), Samsung has removed the UMS (USB Mass Storage) mode from all its devices. Axiomatically, it is not present in Galaxy S4 Zoom. But folks at galaxy phone have found a way on how to enable it.
Basically, what you need to do is get a pre rooted ROM for it and flash it. Then install the UMS utility for the Samsung Galaxy S4 in it and you are good to go.
Continue reading Flash Storage Pen Drive Mode in Galaxy S4 Zoom