If you're going for an award ticket, then looking at revenue tickets like K fares is not relevant. What you need to look for is XY availability (saver coach). You can do this by logging onto ual.com, setting your preferences for "Expert" mode, and then doing a standard award search. This will allow you to see XY availability (or lack of availability) on all itineraries.

If you want to purchase a revenue ticket, just because UAL shows K availability doesn't mean that it is actually selling K seats. UAL rarely sells K seats (SFO/LAX-SYD being a recent exception) - sometimes the K inventory exists to allow one to add additional flight segments to that rare K fare (i.e. SFO-HNL-LAX-SYD) even if you couldn't purchase the specific segments (SFO-HNL-LAX) in K.