Why is the Amazon iOS App allowed by Apple?
By my reading, it doesn't.  Which rule do you think it violates?

Section 11 covers In-App Purchases, which Amazon's app doesn't use, and which are only required for "content, functionality, or services in an App".  Amazon doesn't let you buy anything to extend their app.

Amazon's app also doesn't allow purchasing ebooks, which is their only product (AFAICT) that might be covered by section 11.  They have a note at the bottom of all ebook pages that says "This mobile application does not currently support Kindle downloads, however you may add the item to your Wish List and purchase it using the browser on your device".

Finally, section 20 explicitly prohibits allowing the user to purchase a lottery ticket, which suggests that there is nothing unacceptable about other real-world purchases.  Lots of other apps allow them, too, like eBay.