Registered domain using Route 53, using Cloudflare for DNS, having problems configuring DNS correctly

For poor souls who might have had the same question: you don't need to add NS RRs in Route53 in the hosted zone section. You need to go to your Registered Domains, click the domain you want to modify, and then Add/Edit the name servers there.

Those are the domain NSes, and are associated with the registrar, they are different from the ones delegated inside the zone itself.

When I did this the update was almost instant, the AWS data center is probably next to the Google one :)