Is there any mention of a rule which does not allow a non kohen from wearing the official clothing of a kohen - or kohen gadol?
I have not seen an explicit rule against a non-kohen from wearing the bigdei kehuna . However, based off the Rambam (Klei Mikdash 8:11) and Tosfos (Yoma 69a) it seems that a non-kohen would be prohibited to wear the bigdei kehuna.
The Rambam writes that a kohen can derive benefit from the bigdei kehuna on the day they did the service even while not doing the service.
Tosfos notes that really in truth one shouldn't be allowed to wear the bidgdei kehuna ,rather the second the finish the service they need to take off the bigdei kehuna immediately. However ,Tosfos notes that meilah doesn't apply to bigdei kehuna because the Torah wasn't given to angels ,and would be too hard to take off the second the service is over.
If one takes both sources into account it seems that it is obvious that a non kohen has no right to wear the bigdei kehuna since it was only set aside to be worn for the service,and an exception was only made for a kohen to continue to wear their clothing on the day they served because the Torah wasn't given to angels.