I already contacted the customer service twice about this.
The first answer about where to find the lightning deals on my kindle fire app was jsut generic, telling what lightning deals are and how to claim them.
The second answer refers to using this link http://www.amazon.com/gp/goldbox/
What seems to tell me that I should use the regular web browser.
But I didn't get the answer on where to find the lighting deals within the Kindle fire app.
Does anybody know?