Node access user reference Main Modules:


Node access user reference
Node access node reference
Flags
Rules


I'm trying to give access to a user that clicks on a Join Project flag link.

I have a User Reference Field attached to a node call Project.  I'm wanting to tell Rules to add that user to the Node Access User Reference field, AKA "Join the group"
There is as well:
http://drupal.org/project/nodeaccess_autoreference module
which is working in similar way. But I'm not sure if this solves your problem.