As an alternative to checking the sidecar file, which does rely on the parser that jhowell referenced - you can do this:
- Every time you finish reading a kindle book, search on ";dm" which will dump log messages into a set of log files in the documents directory of the kindle (mountable from a PC without needing to jailbreak).
- In the systems log file that is produced, just filter on rows containing "TimeLeftInBookString:Book complete" - and you'll find the exact moment the book was finished.
- Unfortunately, the kindle masks the ASIN for the book, so you have to know roughly when you finished it if you've completed more than one book recently.