All the store link did was to transfer you to a browser so that you could then browse/buy. You now have to do the switch yourself - just open up Safari (or any other browser that you've got on your iPad and/or computer), go to their site and buy your kindle books, and they should then download to the Kindle app (you may have to tap the Archived Items button bottom left of the app or the icon of the two arrows shaped as a circle bottom right)
The link from the app was removed as Apple wanted 30% of any purchase that was made from 'within' an app - so it was either remove the direct link or pay Apple 30% of what you then buy. All I've done is add a Safari shortcut to the Amazon Kindle store on my homescreen so all I have to do is tap on that to go straight to their ebooks.