Apple's cut doesn't apply to physical goods, which is how the main Amazon app gets by. If you're selling some real widget you're in the clear.

I feel like an idiot for only just realising that this is why eBooks can't be purchased from the Amazon app, but can be from the mobile site.

Stripe already works with several companies that accept payments and bypass Apple's cut, such as OrderAhead and Exec. There are some types of purchases that must go through Apple, however, such as digital goods/content.

Yeah I'm interested in using this to sell physical goods, outside of Apple's domain.