Just show your app/ticket with sky priority printed at the big arch that says KLM/Sky Priority right in front of the departures 2 main entrance, or your Sky Team Elite/Silver Medallion status. I'd strongly suggest getting a taxi from someone like TCA vs taking the train, it's just so much easier and you'll get dropped right off by the sky priority entrance. Then just find the shortest (usually that means nobody at this time) line for check-in and baggage drop-off. If you have odd-sized bags, once tagged, you take them to the right past the priority entrance/stairs to security. If not just take the stairs on the right for priority security where they will check your eligibility before sending up. There's also an elevator which you can use to cheese the line a bit if it's coming down the stairs.

Once through security passport control is either straight ahead or left depending on how you were routed. It's a lot different than TSA and actually makes sense once you see how they do it. But pro tip, if passport control is really long you may be able to walk to the right and down to the other filter if they opened it so don't freak out if the line is stretching waay out to the right. But since OP isn't flying with children they can use the automated passport check so I wouldn't worry about any extra walking.

Then go get a croissant from the bakery down the escalators because you'll be stuck eating some crummy Delta breakfast sandwich otherwise.