Thanks for all the replies!
I think I'm going to go for it.
For everyone asking why I don't just tell him to keep off my kindle - it's a good question. I think I feel uncomfortable doing that too directly, because he's very generous with me pretty much all the time. The most recent example is that he got himself Diablo 3. I got interested in it, but my computer can't handle it - so my SO willingly offered up his desktop computer to me to play on pretty much 50/50 for the few weeks I was really invested. Now, that's a bit different just because buying a whole new computer just to play Diablo 3 is not really reasonable, for either one of us.
Point is, I think I'd feel a lot more comfortable fixing the problem by buying him a Kindle than by just telling him he can't use mine.
If he had a smartphone, the Kindle app would be a great solution, but he's a weird mix of technogeek and luddite, and the cell phone falls in the luddite category.