I hope there is a token appended on the query parameter when using browser flow, so that we can use that token to get identity info

Could you provide more details here? Kratos uses a session cookie which you can use to retrieve user information with on your back-end middleware.

When login success, there is a set-cookie header. but the cookie was set for kratos. the ui site is dev-hodor.test.com the kratos site is dev-krotos.test.com when I access the ui site, no kratos cookie was sent. therefor, I can't get user info