Install Zyzzyva on Linux as normal.
Then copy over these files from Windows in this folder:
C:\Users\<username>\.collinszyzzyva\quiz\data\*
to wherever Linux puts the user data, likely in ~/.collinszyzzyva/quiz/data/
That should do it.
Another option is to keep your cardbox database in the cloud, like Dropbox, then point Zyzzyva to those files using symbolic links. I use Zyzzyva on three different Windows computers, depending where I am, and they all reference my cardbox in a Dropbox folder.
:)