I second the unblock-us.com test.
This seems to be the easiest and least invasive way to change some dns settings in your router and move forward with a kindle fire.
The amazon free prime videos and others work very well. No issues. I'm on a trial run with the site but I plan on paying for it.
I'm using it on a laptop, desktop, Samsung Galaxy 10.1, Kindle Fire and a Wii. I've tried netflix on all of them and it is working like a charm!!! Like Pushka says it works like a treat!! It is a treat to get American netflix. I don't like Brazilian Netflix as it dubs all the kid shows. My son is an English speaker and he needs to reinforce that any way necessary.