Not sure if this was asked, will King Fredrik and Queen Mary's children and future grandchildren be known as Frederik's denomination Kongen af Danmark /King of Denmark as (name followed by) prince/ss Af Danmark?
Frederik isn't using Kongen af Danmark (King of Denmark): Judging by his message to Parliament (see my previous post in this thread); he is following his mother's lead and using Danmarks Konge (Denmark's King).
I'm not sure if I understand your question; are you perhaps asking whether the King is also a Prince of Denmark? If so then no, he is not. The Scandinavian monarchs drop their Prince titles upon becoming Kings.