With the usual heavy dose of assistance from the the Zotero devs, I
put together this little bit of PHP to transfer Zotero-based PDFs to
my Kindle automatically.
https://github.com/stakats/zotero-to-kindle
You specify a Zotero tag (e.g. "Kindle"), and then this code will poll
the API to get the resulting files to send to your
kindle.com address.
I've got it running periodically as a cronjob. It's kind of a mess,
but since it more than gets the job done for my purposes, I'm probably
done with it. In case it's of any interest to others, I put it up on
GitHub (with the necessary dependencies as submodules). -Sean