I very rarely have a need to read away from a light source with my Kindle. However, it does happen from time to time. While camping I always use an LED headlamp for reading. I found a very inexpensive (about $5) solution that is not bulky at all in the Energizer Trim Flex LED. I found this at Target today back with the flashlights. Here's a webpage with all the specifics of this light:
http://ledmuseum.candlepower.us/entrfl.htm
Because it uses the button batteries, and has no AC adapter, this is a light use device. If you need something for every night look for one with a plug.