To play videos of Kindle reader in OSX?
Kindle for Mac is specifically for reading Kindle books, and doesn't handle any other media.  On iOS, the same is available through the Kindle app.

Amazon Cloud Player for Mac is for music purchased in the MP3 store.  Again, there is an Amazon Cloud Player app for iOS as well.

On your Mac, Amazon Instant Video is available through the Amazon website itself.  If you have video in your library, you can access it through Your Video Library.  In general, though, any video you have rights to view (e.g. with Prime Instant Video), you can access by finding it on Amazon's website.  On iOS devices, you can use the Amazon Instant Video app, which also supports AirPlay for playback on an Apple TV (though Amazon does not actually have native video support on Apple TV.)