The way with registry edit to remove file history on Flash is described on the Adobe forum:
https://forums.adobe.com/thread/778451 (same info as @Mynamerr posted only hosted on Adobe’s site).
The steps are:
each previous history is there and you can manually delete. They are called ‘RecentMovie№’.
I believe that if you leave a gap in the history (eg. you delete number 1) then 2 onwards won’t display either. You can renumber manually but it is maybe easiest/laziest to just delete all the ‘RecentMovies’ and start from scratch.
If you use this to cover up hack client and pass yourself off as legit you are needless to say scum.
And I guess for anyone doing hack checks, be aware that just because someone has a clean looking Flash history that is no way proof of anything.