No, KFOR is purely a NATO force. No UN involvement. No bluers.
Yes, it operates (or was supposed to) under the mandate of UNSC 1244, but that’s it.
A parallel civilian UN mission (UNMIK) was established under UNSC 1244, but KFOR is not subordinate to it in any way. Anymore than our troops in Afghanistan were subordinate to a similar UN mission there (UNSC 1378).
UNMIK has by now been reduced to practically nothing, BTW.
“No, KFOR is purely a NATO force. No UN involvement.”
Here is a link showing the make-up of the peacekeeping force in Kosovo (KFOR):
https://en.wikipedia.org/wiki/Kosovo_Force
It is multinational. It was established from United Nations Security Resolution 1244.
There are NATO countries involved as well as non-NATO countries. While KFOR has a NATO command element, KFOR is not specifically a NATO force. It is, in reality, a UN force, as it was created by the UN.