Earlier quoted context omitted.
No, in a regular browser you can make purchases on Amazon like normal. If you attempt to purchase a kindle book from within the kindle app, you will not be able to. Nor will there be any messaging explaining how to make a purchase (because apple does not allow such messaging). You’ll just be mysteriously confused about why you can’t buy a book.
Why can I buy an Audible audiobook directly in the app on iOS (and for cheaper than listed on Amazon), but not a Kindle book?
I'm not surprised, since you can often buy a Kindle + Audible book for cheaper than buying the Audible book alone.
If you look at the Audible book (such as Wool https://www.audible.com/pd/Wool-Audiobook/B0BKR3Y6SP) the price is often higher than if you look at the Kindle book price, and adding the Audible narration (https://www.amazon.com/Wool-Hugh-Howey-ebook/dp/B088SY4GSD).
In the Wool example, the Audible book is $31.64, but the Kindle book with the audible add-on is $9.48 ($1.99 + $7.49). Even if the Kindle book was selling for "list price", it would still be cheaper at $27.48.
So, I'm guessing there's just a lot less margin headroom to eat a 30% cut on Kindle prices, but plenty to eat that on Audible's prices.