Moving this discussion to the Installing Flash Player forum.
This depends on your version of the Kindle, but I'd first check the Kindle store (or for any Kindle software updates.) If you're using a Kindle Fire HD, please note that this 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.