Your Kindle uses Android OS.
Adobe stopped ALL development of Flash for Android last year.
There are older versions of Flash Player (for Android) at that link, but there are no guarantees any of them will work.
See also: http://forums.adobe.com/thread/1061194
I've read a lot about "Dolphin" for Android https://play.google.com/store/apps/details?id=mobi.mgeek.TunnyBrowser
I'm not an Android user (no tablet or phone) so I can't make any endorsements that would hold any credibility, but most of the Flash solutions I've read point to Dolphin as the best alternative.
Check the Android forums: http://androidforums.com/ to see what their "gurus" recommend.