He almost certainly has regular CoC.
I believe that for a few reasons, including his (lack) of reactions to Zoro using it, his attacks having the kanji for emperor in them, his name.
50/50 on advanced CoC. King is definitely going to compete with Advanced CoC Zoro on even footing in the next few chapters tho.
However, I can also see Oda choosing to focus on King's racial abilities instead of his haki traits. We just need to wait and see.