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.
Great question and thanks chris with the follow up. I was looking at which kindle fire I should buy. I was stuck between the regular version and the HD version. I've been doing my "research" and learning as much as possible.
Thanks again for the info!