Meanwhile, the ChromeOS release of Chromium has had support for FLAC for a long time, but it's still feature gated on mainline Chrome.
4 year old issue: https://bugs.chromium.org/p/chromium/issues/detail?id=93887
4 year old issue: https://bugs.chromium.org/p/chromium/issues/detail?id=93887
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/