How to automatically remove Flash history/privacy trail? Or stop Flash from storing it?

If you use Firefox then you have the BetterPrivacy extension. It removes LSOs during exit. And of course you can use Flashblock or NoScript for additional security.

Update: Since 10.1 Flash doesn't store LSOs if you're in private browsing mode.

I implemented the solution you described on Mac a few months ago. It did prevent the tracking, but it prevented quite a few more complicated Flash applications (anything with persistence between sessions, most obviously Flash games with progress tracking) from operating correctly, or at all. Eventually I got tired of troubleshooting and removed the folder locks.

My interim solution is using a Flash blocker. As I only load Flash objects for sites I trust (such as YouTube) the privacy concerns are mitigated, if not removed.

I think on Windows CCleaner will clear it out.