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).
They don’t have to wear blue helmets to serve a UN function.
Blue helmets mean they are under UN command; KFOR — while a UN mission — is under NATO command. Operation Desert Storm in 1991 was authorized by UN Resolution 678, but it was not under UN command.
KFOR is acting pursuant to UN Resolution 1244; NATO didn’t create that. And you conflate the respective functions and purposes of EULEX and UNMIK and KFOR: They are different (yet all three are based on UN Resolution 1244).