One of the major shortcomings on Apple's ecosystem is that it's very much geared toward Apple services. While you can purchase all of the content that you want through iTunes, Books, and more, many third-party providers don't let you do so. The reason is because they don't want to pay the 30% "Apple Tax", which takes a cut of sales on digital goods.
One of those companies was Amazon, but that's starting to change today. As of now, you can purchase or rent content from right within the Prime Video app on iOS, iPadOS, and tvOS, something that Android users have been able to enjoy since the app was introduced.
Previously, the app only served as a way to playback content that you already have access to, whether that access comes via purchase, a Prime Video subscription, a channel subscription, etc. If you pulled up a listing for something that you did not have access to, there were no further instructions, as per Apple's rules. The user would have to launch Safari (or any browser), navigate to Amazon's website, purchase the content, and then return to the app.
Unfortunately, this change isn't yet being made on Amazon's other services. Things like Kindle, Comixology, and Audible all require you to purchase the content externally. We've reached out to Amazon for comment on this, but haven't yet received any response.