I only use part of HK's definition of hula hula flexibility.
He states-: "A Hula Hula flexibility allows the Hips and Shoulders to be independent but coordinate."
I simply think of hula hula flexibility as the ability to rotate your pelvis in the downswing without necessarily rotating your shoulders concurrently in the same direction.
Here is a nice practical demonstration of excellent hula hula flexibility where the dancer can move her pelvis in one direction while she moves her upper torso in the opposite direction.