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No, you don't need to contact Amazon to redownload your books and apps. All you have to do is, register the new Kindle with the same Amazon account you used on your previous Kindles. This is very important.
Setup your Kindle and make sure you register it with the same Amazon account you used on your previous Kindles. After registering it, open the Amazon App Store app. Tap My Apps at the bottom. Tap Cloud tab and you will see all your purchased apps. Tap the Download button to download them to your new Kindle.
Refer this article --> http://groovyandroid.com/how-to-update-manage-reinstall-apps-amazon-app-store-1608/
To redowload your books, open Books. Tap Cloud or Archived and you will find your books there. You can download them from there without paying again.
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