Cloudflare doesn’t support subdomains, so no. You’ll need to get a custom domain name for that.
What’s that referring to?
Cloudflare has never supported subdomains. Free domains are still supported by us and by Cloudflare.
The only thing we did is remove our Cloudflare integration because it was troubled. But you can just use Cloudflare yourself. It’s something you can use to setup your website, it’s not a hosting feature.
If you are referring to free subdomains, then no. Cloudflare doesn’t accept them and we don’t let you use custom nameservers for it.
If you’re referring to a custom domain you happened to get for free, then you can change the nameservers in the same way you did when you set your domain up with us.
I had added a few free domains from Freenom to Cloudflare.
Sometimes, Cloudflare says lookup failed but keep trying.
I noticed newly registered free domain can’t be immediately added to Cloudflare.
Maybe you can try after a few days.