This is no longer being developed since Netflix implemented auto play for Chromecast.
Netflix-autoplay-for-Chromecast
Currently it will move to the next episode, but it will not cast the tab. I'm convinced it's possible but I'm having a hard time figuring it out.
For this to work correctly you need start on the episode listing, for example: http://www.netflix.com/WiMovie/70185133?trkid=13462050
Installation:
Netflix autoplay for Chromecast is a Google Chrome extension.
- Click here to download.
- Unzip download.
- Navigate to chrome://extensions
- Expand the developer dropdown menu and click "Load Unpacked Extension"
- Navigate to the unzipped plugin and hit select!