I successfully bought a book using my iPhone while travelling. Unlike previous similar occasions, I seem unable to now download it to my Kindle or iPad as well. If I go to the Store there is no message that “You own this book” etc.
Check which Amazon account your iPhone is connected to - and check what Amazon portal you purchased it from when travelling (America? Germany?)
If the answer does not leap out at you then contact Amazon using the HELP link on every page. The help desk will ask you to confirm the EXACT Amazon login you use on your iPhone and other devices, and then may be able to explain things to you or assist you.
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I wonder why someone would follow their own alternative forum profile.
log into your account on the amazon website using a browser
select Manage Your Content and Devices from the upper right menu
see if the book is there
if it is and all 300 of your other books are there, then select Devices and see if both devices are listed there. You should then be able to go back to the Content tab and send the book to yoru other device. If it's greyed out, it's not compatible with the 2nd device
if it's not, then your second device is not registered to the same account as your iPhone