Gosh, I didn't even know that PKZIP was still around.
It started as a DOS program and is now a Windows program; it will not run on Linux.
You might try
7zip with
Wine. The Wine applications database reports that
it works very nicely with Wine. Wine should be in the Ubuntu repos.
You'll need to read up a bit on how to use Wine to do so, but it's not that difficult assuming the Windows application works with it.
Googling for "multipart zips linux" did not turn up a quick solution. Linux's native zip program doesn't seem to be friendly to multipart zips.