So the problem is really the Kindle app on the iPhone.
It might sound obvious but I get glitches with the iPhone apps at times and usually just switching the iPhone off and then restarting it fixes the problem. Although I have to say that iPhone apps do tend to be quite buggy - the amount of times my web browser just quits without warning is ridiculous but I've had no real problems with the Kindle app.
If you don't get any joy in this forum also try asking in the relevant apple forum on mobileread.
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