Android is just the os. On top of that there are various services and apps, like google play, google maps etc. Amazon kindel devices don't use google services, they provide their own. This means that you need to have 2 versions of your app, one for each platform.
Amazon provides documentation on using ADM https://developer.amazon.com/sdk/adm.html
If you managed to get GCM workin then you won't have any problems with ADM. Similar philosophy just different implementation.