I just did some updates on my books and had to republish them. Kindle will only email customers about the book updates if there is a "major change".
As I am not sure what is considered a major change, I've decided to give you a quick tutorial on how to update your books on the kindle!
On your computer, log in to your amazon. At the top right it will say "Hello, Your Name" and "Your Account". When you hover over that a drop-down menu appears. Go to "Manage Your Kindle".
Now, there are two options: They now have Automatic Book Update.
All you have to do is click on "Learn More" and then make sure the option is turned On.
That's it! It should automatically update your books!
If you don't do that, then you can search for the book and see if there is an update for it.
It will tell you next to the title if there is an update available. Click on the actions button to the right and and drop down menu will appear. Click on "Update this title".
Once it is updated it will tell you that a new copy is being sent to your kindle!
The next time you open and sync your kindle, it will automatically update and you will get your new copy of your book!
I hope this helps!!!