Question: I am a Professor at a college in the US where we wear regalia to the student graduations. I have a PhD, but am about to complete another doctoral degree from a different university, neither of which are where I teach. Do I have to choose one gown to wear to graduation or is there a specific way to represent both degrees? I have yet to find any guidance on this!

Answer: 
As no one who matters will actually know which degrees you hold and what gown goes with which, the choice of gown will be yours! If you own both, choose the one that is the most distinctive, colourful, or photogenic.

That is what your graduands and their families would want for their photographs.

(If you only own one, then the choice has already been made for you.)
@Ragaroni's answer seems good for the US. Here in England-and-Wales, there are no intercollegiate rules and it would be a question for the internal regulations of the university hosting the graduation ceremony.