Multi-tenancy at the data level exists if you pair Kibana/Elasticsearch with Shield - you can restrict which users can view which data in Elasticsearch at a pretty granular level. However, fine-grained access control at the UI level, such as restricting which dashboards and views are accessible to given groups of users, is not part of that integration yet.
You can work around this currently by setting up multiple instances of Kibana - one per user - configured to point to different configuration indices (instead of the default .kibana).