UPDATE:
This used to be easy - but with Flashplayer support ending in 2020, and with Google Sites changing to the NEW format, this tutorial isn't terribly useful anymore.
The workaround:
If your animation is silent, export the animation as an animated gif and insert THAT into your webpage - it's very simple, but doesn't accommodate sound or more than 256 colours.
Meanwhile, I hope to learn how to export animations from Adobe Animate CC in HTML5 and embed THAT into the new google sites. Stay tuned.