How Do I Create Sub-Sub-Domain on Cloudflare DNS?

• In Cloudflare, open the DNS records for domain.example
• Create a A record for example.id and enter the IP where my.id.domain.example will be hosted, and add record
• Setup the site my.id.domain.example at the IP you specified

If domain.example is on Cloudflare and the Cloudflare nameservers have propagated, the sub-sub domain propagation should be more or less instant

As correctly noted by ThorSummoner and user296526, this will work on the Cloudflare free plan if you aren’t using SSL.

If you want to have a sub sub domain with SSL on Cloudflare, you need to a dedicated Cloudflare dedicated SSL certificate which is available as a paid plan. To quote from the Cloudflare site:

Cloudflare Dedicated Certificate with Custom Hostname: $10 per domain
per month

Includes all benefits mentioned above for Dedicated Certificates
Protects your domain, subdomains (*.example.com), as well as up to 50
additional hostnames Can extend protection beyond first-level
subdomains (*.www.example.com, not just *.example.com) Dedicated SSL
certificates typically provision within a few minutes but can take up
to 24 hours.

Full details here