Can I move my kindle books over to my iPhone?

I already have the kindle app and everything, but I just don't like the setup as much as I do the iBooks setup. Is there someway to download the book to my iPhone without having to purchase it again?

Yes - install the Kindle reader app on your iPhone. Register it to the same Amazon account as the Kindle. Now onnect your iPhone to a Wi-Fi network if you can (for receiving the books).

Then, if you bought the Kindle books at Amazon, just go to Manage Your Kindle at Amazon (here is US link):
https://www.amazon.com/...yourkindle

Find the books in Manage Your Kindle and to the right of each select Deliver To… And pick the Kindle reader app on the iPhone. Now that book will be delivered to your iPhone wirelessly.

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If you got the ebooks elsewhere, then you need to manually transfer them.
Some instructions in comments here
http://forums.imore.com/iphone-4s/228562-sideload-ebooks-kindle-app.html

Once you buy a Kindle eBook, it's yours to read on any device you have, as long as you can install the Kindle App on that device.

Simply register that app to the same Amazon.com account and re-download the books you bought to the new device.