You should have no issues whatsoever. Don't enter any queues outside or in the building, just make sure to get inside the departure terminal. Everything is connected inside, so it really doesn't matter where you enter the terminal building. You can enter directly from the train platforms onto Schiphol Plaza, through the doors on level 0 into Schiphol Plaza or through the doors on level 1 directly into the departures area. Other entry routes are from the concourse to the P1 parking garage and airport Hilton hotel.

Whatever your entry route is, just follow the signs to "Departures 2" and follow the SkyPriority signs there. There will be KLM staff at the entrance to the SkyPriority area checking your ellgibility - which is either a paper or digital boarding pass with SkyPriority logo or a quick show of your Skymiles card in the Delta app.

There is an escalator going up directly from the SkyPriority checkin area which brings you to security, completely seperate from the regular route and queues. The only queue you might see is right after security, where you join back with all other security lanes for exit immigrations. With a US passport, you'll need to enter the middle lane leading to the manned immigrations booths. FYI: the left lane is for the electronic gates, which are only for EU passport holders. The right lane is for crew, diplomats and the automated immigrations gate for pre-cleared members of the Privium program.

When you get through security, take the escalator down, turn to your right for a full 180 degrees and walk towards the "E" gates. About 3/4 of the way in between the "D" and "E" concourses, you'll see two escalators on your right with loads of KLM Delfts blue houses lining the walls. That is the entrance to the KLM crown lounge. Take the escalator up and scan your boarding pass at the automated kiosks for entry.