For now, you can accomplish what you want to do with the Security feature in X-Pack. You can configure different roles, which you can assign to your users. Each role can be configured to have access to certain indices. If a user views a dashboard that contains a visualization which references a disallowed index (based on their role's permissions), then it will just show up blank.
Here's more info on how Security works in X-Pack: https://www.elastic.co/guide/en/x-pack/current/authorization.html
Note that this is a short-term problem, and in the long-term we'll be focusing on object-level security which will prevent the blank visualization from showing up in the dashboard at all, if the user isn't allowed to see it.
Please let me know if this helps!