“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.
Yes, it was authorized by UNSC 1244, and is supposed to carry out that mandate. But it is not a UN operation, is not part of UNMIK (ths UN civilian mission there) and is entirely under the command of NATO:
https://shape.nato.int/ongoingoperations/nato-mission-in-kosovo-kfor-
https://jfcnaples.nato.int/kfor
Again, KFOR is strictly a NATO mission, not part of a UN mission. It works alongside EULEX (the EU mission in Kosovo) and UNMIK (UN mission which has been drawn down to practically nothing now), but is subordinate to neither.
Yes, there are a few soldiers from non-NATO countries,* but they are under NATO command:
https://jfcnaples.nato.int/kfor/about-us/welcome-to-kfor/contributing-nations
None of these guys wear blue helmets or berets or have the UN patch on their uniforms, and none of their structures or vehicles fly the UN flag.
*Mainly for political reasons and as window dressing in the beginning, and to ensure passage of 1244 even though the US certainly had the catbird seat in the SC at the time and got pretty much whatever it dictated, but some things are a bridge too far. Remember, the 1999 bombing of Serbia was not authorized by any UNSC, and was in violation of both the UN Charter and the NATO Charter (and broke the Peace of Westphalia we used to go on about — inviolable national borders and all that — and set a dangerous precedent).