Refer.ly itself won't be able to be "gamed", they will only pay out a commission for a made sale, so there is no risk to them. Are you talking about someone "gaming" other user's links and replacing the original placer's tracking id with the gamer's?
The Amazon problem could be harder to manage as they scale since they can't do subid tracking per user and probably try and correlate redirects to specific Amazon purchases, but that is going to leave a lot of grey area for any other purchases the user should be credited for but turns out to be too difficult to correlate.
Sorry, I should have clarified. First, your site is brilliant in that it captures something that happens ALL THE TIME; people referring products to their friends. It's arguably the best way to push product in today's global web-based market. But there's an underlying problem; you've now are converting people's value of sharing into money. Once this catches on and gains real customer acquisition power, you know someone with a bigger wallet will be all over this trying to push their product. So, then at some point, my "friend" recommends a product/service, but I notice their getting a cut of the action. What are their real intentions? Is this something they genuinely are recommending?
Additionally, since you take no cut of the affiliate payment, I'm trying to find out who you're actual customer is?
(note - that doesn't mean they can't make money. Looks like a pump-n-dump to me)