Having taken multiple connections in ICN where I was on KE, but seated in Y, my boarding pass always reflected "Sky Priority / Sky Team Elite Plus" (as I'm PM). The KE GA's usually came through checking everyone's BP and more than once they saw the Y seat number and tried to direct to me to the "regular" line, but when I pointed to the Sky Priority/Sky Team Elite Plus wording they immediately nodded and apologized. So, the moral is if you are on a DL metal flight, DL's rules should apply. If you are on KE, then your BP will need some sort of verbiage indicating you qualify for premium boarding, otherwise I would expect the regular line.