I would've imagined Netflix had their own hardware, both compute and storage.
They use AWS for video transcoding) (see http://techblog.netflix.com/2015/12/high-quality-video-encod...) and probably other activities (analytics, business)
There are also kubernetes and mesosphere to do similar thing, but they are harder to use, you can't learn them over a week end.
Netflix runs their OpenConnect appliances at every big ISP that will let them put one there:
https://openconnect.netflix.com/en/
They run Freebsd, and all of the web services (thousands of them) run in AWS on Linux.
https://www.rapidtvnews.com/2016031942170/netflix-moves-all-...