When you tap on a book to purchase in the kindle app, there is a disclaimer in the title page saying the App does not allow purchases. But if you login to a browser and purchase, then sync the Kindle App Library, books will be there in the Kindle App Library to be read.
But you’ve always had to make purchases outside of the App, to my knowledge at least in-app purchasing was never supported. Same thing with the Barnes and Noble Nook App. You have to purchase from the web site, then sync the App Library to get new purchases into the app.
I’ve never subscribed to Kindle Unlimited, but I would assume anything you add online to your Amazon account library under that subscription should sync to the App Library? At least from the Kindle App reviews in the App Store, people are using the App with Kindle Unlimited subscriptions.