How to register a new domain name?
At this time, you can only transfer existing domain names into Cloudflare. These would be domains you already have on a plan here.
You need to add that domain to Cloudflare, configure it and make it working and then change the registrar.
It would be great if we could buy the domains directly in Cloudflare
Yep. Someday that will happen. I think top of their list is getting a bunch of ccTLDs approved for transfer. New registrations should come after that.