Denmark entry by US citiezen

According to the rules TODAY--they could change by September--you just need your CDC card.

TLDR Frank II beat me to it, I just gave a slightly longer answer

I'm assuming that you're a US resident - the Danish COVID travel restrictions doesn't care about your citizenship (unless that's a Danish citizenship).

One thing we've learned from the last 1,5 years is how quickly entry requirements can change, but currently: Yes, your CDC vaccination card is enough. Both the US and the Netherlands are currently "yellow" countries, which is the secondmost safe ranking, meaning no testing or isolation needed when you're fully vaccinated with an EMA approved vaccine.

The interactive guide in the dark blue box on https://en.coronasmitte.dk/covidtravelrules/ can give you a quick overview of the current rules.

If you can prove that you are fully vaccinated with an EMA-approved vaccine you should not need a test as long as you have not been in a red country recently. At the moment, Russia and the UK (except Wales) are the only red countries in Europe, but that can change.

I think it is prudent to add, that given your itinerary, the Danish authorities would be concerned that 1: you were in the US in the last 14 Days. 2: You were in the Netherlands. They then would apply the most stringent requirements that apply at the time of entry to Denmark from either Country. Denmark is part of the EU and the Schengen Agreement, so unless you have citizenship in one of the member countries, nationality does not apply.

As others mentioned, this even applies if suddenly rules change in the four days you are in Amsterdam.