They really don’t explain how Kylo knows where she is going, do they? I assumed they put a tracking device on the Falcon, or they tracked them through hyperspace, but they didn’t follow them. But I don’t think they ever clarify it. Maybe the Emperor told him where the Wayfinder is, since it is HIS Wayfinder, but Kylo tells him, “I know where she’s going.” as if the Emperor doesn’t know where she’s going (didn’t Hal move this scene up to a place where it makes sense?)
My most recent theory is that Kylo can read Sith, so he must’ve read it at some point while it was in his chambers. But again, I don’t think the film really explicitly tells us.