We are talking about separate tickets here.

As AMS-CPH-AMS is on its own ticket, KLM is the "MSC" and KLM's baggage rules apply entirely.

It is not clear how you booked the ticket, or why you didn't book AMS-CPH-AMS on the same ticket. If it had been a Flying Blue redemption, such EU sectors should have been available for the same price.

If you only have one bag, and this is less than 23kg/50lb, then this will go for free on KLM thanks to your Delta status (be sure to carry your card).

As stated above, KLM may not check your bag all the way through on the return, but if you check in at the business class/SkyPriority desk and show your status, your chances of having it checked through are enhanced.

Just make sure you check with ground staff at AMS that the bag is in the system; show them the luggage tag. When checking bags between tickets like that - which is not supposed to happen - there is always a chance that your bag will get lost.