I suspect the KE app will probably issue you passes for both segments... If you don’t have a pass yet on arrival into ICN, I believe there are transfer desks in the immigration hall that can print you one. Note ICN flights inbound to the US may require the usual passport sticker interview, so keep your eyes peeled for that at the gate.

KE’s checkin in HKG is friendly and efficient - I’d honestly suggest that you just get a set of paper passes there, as they will definitely be able to print the onward pass. You’ll have to walk by the desks anyway to get to security, and then there won’t be any stress about the various apps. Only takes a few moments at a time when you're about to just sit and wait anyway, and paper is better anyway because it can’t run out of batteries and can be easily submitted for missing mileage credit.