I selected the Kindle Fire HD as the promotion item when we recently signed up for U-verse. When I attempted to watch U-verse movies I was prompted to load Adobe Flash Player. I seems that the Kindle fire will not run Flash Player, but uses another system routing content that requires Flash player through another process. The Amazon information states that this is only compatible with a limited number of content.
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I don't know if this will make a difference, but go to Adobe.com and check the knowledge base, or support there for an answer. I downloaded my flash player from there so you might try that if you haven't already.