Unless there's some new feature I don't know about, this would have to be done in a different software and then brought in as an Alembic file, or sent over as an animation using one of the plugins. Keyshot itself won't create linkages.
It's possible to animate it in keyshot (without linkages) but your grouping has to be perfect before you start animating, and your timing has to be spot on for it to work. This would be a lot of rotation and translation animations all thrown in simultaneously. Would be very difficult and time-consuming.