Cloudflare is a DNS level CDN. All you need to do is change your Domain name server to theirs and their will take care of lot of caching and distribution.

The problem is that when you’re using AWS Route 53 you may notice that your Name servers get reset back to AWS ones in couple of days.

This is due to fact that Route 53 has 2 places where you need to configure NS.

Most of us configure the NS in “Hosted Zones”

But you also need to go to your Registered Domains, click the domain you want to modify, and then Add/Edit the name servers there.