Question

How did kenneth clark know of the african dancing mask he disparaged in his television series and book civilization?

Answer 1

he owned it.
   When something is familiar to you, one is bound to know the everything about that item, so the issue of Kenneth Clark not taking or regarding the dancing mask to be of much value must have been that he used it for years and have become tired of it or believes it's of very little value to him because it had probably served its purpose well enough.