Any other way to authenticate in embed

Technically none.

As docmuneted:

Is the “proper”/official way to embed chat, which will handle authentication on it’s own. The alternative is to essentially build an entire IRC client inside you app, and rebuild the whole chat experience, which then means you’ll be behind whenever Twitch pushes a new thing. And additionally you’d need to request some hefty WARNING permissions from the end user

(I saw warning as they’ll be DANGER flagged on the auth dialog)

Make sure you protect your secrets and there is no way to extract the client secret from your App. The use of OAuth Implicit Code Flow may be more secure here.