Amazon has updated it: Kindle app for iOS and removed the button to take readers to its Kindle Store.
Note: It doesn't seem that you have to upgrade, so if you don't want the Facebook and Twitter integration, you can stick with the old version for now.
Earlier this month it had seemed as though the button that gave users easy access to the Kindle Store was here to stay, but it seems that Apple's updated guidelines DO apply to Amazon, and this button in particular.
Along with removing the button, Amazon has added Facebook and Twitter integration to allow the easy sharing of quotes and passages with friends and followers.
Has Apple won? I don't think so. It's easy enough to fire up the browser and type www.amazon.com ... this change isn't going to make me switch to the iBooks store.