Early on in the Netflix streaming there was a trick you could use to capture the streamed video and save it as a video file. This wassoon 'fixed' and Netflix has been using DRMto prevent capturing the video. It isn't like trying to copy a Youtube video. Sorry.
Amazon will should let you cache a rented movie (but I am not really sure), but it will still be DRM'd.
Or, you could just rip a DVD with the software of your choice (an old copy of DVD X Copy still works for me),and then play in the video player app of your choice. (I like Moboplayer)