Ok, you approach this in a mature way, which adds in building on your credibility.
Now, if you could somehow prove to buyers that you have a long standing account with Amazon, and that the credit card you use with Amazon also have been registered a long time ago, then this also may add to your credibility. If this is a new idea of yours, and you just recently registered with amazon, and you haven't yet done any purchases there, or only a few, that would be a very good reason to have eyebrows raised.
Would it be possible to do some partnership program with Amazon that could bring some more light of legitimacy to this business.
You probably understand that the reason newcomers are asked very hard questions, and that there's problematic to get trust is that on the first hand you're new, and on the other hand that you're dealing with some easily reversible payment option.
Now, if we look away from the fact that you might be a scammer, and assume you're a perfectly legitimate customer of amazon that will help people do btc > amazon purchases, then you need to somehow build confidence. And there's nothing better than just starting, and proving to the community that you're trustworthy.
Although I've never met certain people, I would trust them to hold btc. Two names comes immediately to mind: Gavin (head dev) and Casascius (
https://www.casascius.com/). Sturles also is a reputable trader. As for the first purchases from you, they could be small, to build up confidence.
Also linking one's shipping address to some random dude's CC on amazon, how would it turn out if there was something nefarious going on. Customers needs to feel safe.
If you're serious about this idea, I think perhaps making a website to offer your services and writing a faq to adress the concerns would be a good idea.
Please check this list to see what bitcoin businesses exist already:
https://en.bitcoin.it/wiki/TradePerhaps if you search for amazon, you will see someone offering something similar to your services already. But that doesn't mean you should give up, there's always room for more businesses in the same segment.