I need Flash Player for my Kindle Fire and Nexus 7 tablets. When will this be available?

The latest Kindle Fire HD is not officially supported by Flash Player.  Please see this page for a list of all certified devices:

http://www.adobe.com/devnet-apps/flashruntimes/certified-devices.html

That said, some users have been able to get Flash Player working on the Kindle Fire by using Dolphin, a third party browser.

http://www.ccl-la.com/blog/index.php/how-to-install-adobe-flash-on-your-kindle-fire-hd/ 

http://www.youtube.com/watch?v=LF3VCtn4jVM

It won't... Kindles use Android

Adobe stopped ALL development of Flash for Android last year. (July 2012)

http://helpx.adobe.com/flash-player/kb/archived-flash-player-versions.html

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.