You can't run a rule programmatically, unless you are referring to a macro
that is run by the "Run a script" option of a rule.

Regardless, you would have to monitor the MailItem_PropertyChange event and
trap when the FlagStatus property has changed (to olFlagMarked).

See this article for an explanation of how to do this:

Getting a Handle on Your E-mails with VBA:
http://blogs.officezealot.com/legault/articles/2224.aspx

However, you'll have to go further still.  The code above is only good if
the user has opened the e-mail.  Remember, you can flag a message in the
folder view.  So to trap that, you'll need to monitor the
Explorer_SelectionChange event to get a handle to individual Inspectors as
the user selects them; then you monitor each of the items selected for the
PropertyChange event.  This is best handled using an Inspector Wrapper:

Slovak Technical Services Code Samples:
http://www.slovaktech.com/code_samples.htm#InspectorWrapper