Two thoughts. One, as stated above, they should appear in your archive. They will probably not show up in your library at first. There should be an option called archived items, possibly with a number in brackets.
Alternatively, login to the Amazon website to manage your Kindle. You should be able to see here if the iPhone Kindle app is registered at all. Also, there should be a list of purchased books and the option to deliver them to any registered device.
I've had this work on two iPads, two PCs and an Android tab and there is no trick to it. If it does not play ball as expected though, you may have to contact Amazon for support.