Fine-grained flag permissions
Are you looking for a 'local' flag? Flags are already separated into global and local flags. For example, a global flag might be 'report this comment' and once one person flags the comment it is flagged for everyone. Local flags on the other hand are unique for each user, so for example a 'bookmark this' flag would only be for the current user context and other users wouldn't be able to modify their flags. From the documentation:


  Flags may be per-user, meaning that each user can mark an item
  individually, or global, meaning that the item is either marked or it
  is not marked, and any user who changes that changes it for everyone.


You set whether a flag is global or local when you create it.