First, follow this:
http://docs.flexunit.org/index.php?title=Setting_up_a_FlexUnit_4_Project
However, you are never going to be able to click any of the 'Run FlexUnit Tests' buttons in Flash Builder. Those don't have anything to do with FlexUnit... they invoke the functionality that, as you noted, is only available inside of the Premium edition.
However, if you follow the directions on the page above, you will be able to run these tests, it will just be in a separate browser window. So, you will never be able to run them in the FlexUnit Results window, etc... that is a premium feature offered by Adobe and not part of this project, but you can run them.
Mike