Are humans fleishik or are they on a different level? If I were to have a cut in my mouth, would that make me fleishik?
The Rema Yoreh Deah 79:1 says it is assur min HaTorah. Since it is assur I would assume it falls into the same category as a non-kosher animal which the Shach 87:3 says there is no issur basar b'chalav because it was assur from the Torah already.Since it has an issur of non-kosher the other halachos of kosher are not applicable. This is all on assumption no full-proof rye'a.