Kindle Exporter
I'm a huge fan of my Kindle and a huge fan of Papers.app, so I wrote a plugin for exporting papers to the Kindle.
It exports the selected papers' PDF files into the documents/Papers folder of the Kindle.
Installation
Download KindleExporter.exporter.zip, unzip and place in ~/Library/Application Support/Papers/Plugins/Exporters/.
Usage
After installing, you may choose File -> Export -> Kindle. The selected papers will be saved on the Kindle.
Hacking
The source is available. Patches are welcome.