Very sorry for the trouble.  We run into this on occasion.  If you go into the amazon app store and tap the refresh button you should then be able to find the update under "updates available".

If that doesn't work you can go into your phone's Settings> Applications> Amazon App Store. Inside there  
clear both the cache and the data. Then go back into the Amazon App Store. It will ask you to login again.  After that the update should be there.

Best Regards,
Matthew S
BabyESP Support