You can use these two commands to crank up the recording volume before actually running arecord:
/usr/bin/amixer sset 'MIXINL PGA',0 100% unmute cap
/usr/bin/amixer sset 'Capture',0 100%,100% unmute cap
# then arecord
I found the mixer name by trial and error, and I'm not sure if all the parameters are really required. Anyway, this works on my device, and probably should on yours, but you never know.
The resulting files are still not over-the-top quality, but it's usable for taking spoken notes. I'm attaching a sample (recorded from a computer sitting next to the Kindle, playing at "normal" volume).