If you made the original in-app purchases via the Amazon app store you will need to install the Amazon App store onto your Android tablet. 

Launch the Amazon app store on your Android tablet and log in with your Amazon account. Once you have logged into the Amazon app store on the tablet you should be able to install the app as usual and the purchases should automatically restore. 

Here is the link to the Amazon app store with instructions for installation: http://www.amazon.com/gp/mas/get-appstore/android