There's a 'MiracleCast' implementation for Linux. I'm not sure how mature it is but it aims to stream to and from your desktop.
I've been following the project for a while and the answer, unfortunately, is "not very". It does actually work as a sink (WiFi P2P discovery included) and there's a WIP branch with source support (eg for sending your screen to another device).
IIRC it still requires exclusive control over your WiFi card so it doesn't play nice with NetworkManager or similar, and it's just all around just not really ready for casual use. The main dev has been great though and the core functionality is shaping up nicely.