The first way is by using the websites, Aozora-bunko（青空文庫） and Aozora-kindoru（青空キンドル）. At Aozora-bunko, you can get Japanese texts that is out of copyright with free. And you can convert a text into a PDF file that is written in vertical direction by using Aozora-kindle. I have downloaded some books into my Kindle. They includes Terada Torahiko's（寺田寅彦） essays and Kikuchi Kan's（菊池寛） novels.
The second is for my business. I often see some documents about my work. They includes laws and rules in particular fields. I can see these documents on my Kindle by sending text files or PDF files to my own kindle's e-mail address.
Kindle is a interesting device, but my hope is to be able to read newly published Japanese books by it.