How to update a views row class in real time clicking a Flag (ajax) link
Add a javascript file to your theme, or if you're using a theme that has a template, use that.  Omega 4 has a brilliant template file with explanations on how it works and a short example.  There is also a very good tutorial on using javascript and JQuery with Drupal on Drupal.org.

Basically I would set a click event on the flag checkbox and then use the .closest() method to find the row which the checkbox is inside and add or subtract classes accordingly.