The latest Kindle Fire HD is not officially supported by Flash Player. Please see this page for a list of all certified devices:
That said, some users have been able to get Flash Player working on the Kindle Fire by using Dolphin, a third party browser.
The first gen kindle fire comes preinstalled with Flash, so you can just toggle the settings. But all other gens require installing flash and the dolphin browser. Check out this site for more info:http://kindlefiretuts.com/how-to-install-flash-to-the-kindle-fire-all- gens/