There is a kindle app in the droid platform, so you are good to go there. As far as movies, I know you cannot stream from Amazon Prime, because this version of Android does not support Flash. I never tried purchasing and downloading. I expect Amazon really doesn't care, because they are trying to peddle Kindles. The truly only major downfall I found in this tablet is the lack of Flash.
The Kindle app is already pre-loaded. You should register your device on Amazon and your Kindle books will download with a sync. There is a workaround for Flash, although as someone discovered two questions down, all of a sudden (in the last free days) some of us started having problems with it. Watch that Question to see if a resolution is found. If you want to download music or App Store from Amazon, you'll need to allow 3rd party apps on your tablet first. Then you can download the apps from here on Amazon.