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Download the kindle app from App Store in the iPhone; then, use the same account in both apps (mac and iPhone).

Once you have kindle app in the iPhone, you can also send the books from amazon.com
 
Download the kindle app from App Store in the iPhone; then, use the same account in both apps (mac and iPhone).

Once you have kindle app in the iPhone, you can also send the books from amazon.com

See, I tried this. I didn't download any of mine through amazon so that might the be problem. There's a button that says upload collection, I've clicked it and it pops up a screen that prompts me to select a device to upload from, but there are no choices..
 
Plug your phone in to iTunes go to the apps on you phone and click the downloaded kindle app. Then "Add" the ebooks directly to your phone. Worked for me. Added over 2500 to my iPad
 
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