like anything else, if a group purporting to teach CAtholic doctrine or form an association of lay CAtholics attempts to organize in a diocese the bishop has jurisdiction over them, and they must have his permission to operate. That does not prevent anybody from printing a letterhead, sending out a mailing or creating a website and calling themselves anything they want. Never heard of kairos, except as a retreat offered for students in Jesuit high schools, and the ones I know had very good, fruitful experiences. If there is an ecumenical group called Kairos I would need more details.