The Chromecast can receive and play FLAC since 2015 (I can't find the exact dates on any release notes but [1][2]).

This is about adding audio/flac decoding into Chrome; meanwhile the Chrome -> Chromecast communication is entirely proprietary (notwithstanding the APIs), so Google controls both ends. Since so much of the Chromecast is about handing off content [3], there's little need to implement FLAC encoding in Chrome because the Chromecast can just be told to load the native (original) stream itself.

[1] https://www.reddit.com/r/Chromecast/comments/3n1to8/chromeca... [2] https://www.reddit.com/r/Chromecast/comments/3n3epm/flac_is_...

[3] (Annoying ad warning but good content) http://www.digitaltrends.com/computing/chromecast-features/