CNAME setup is a manual process available to paid Cloudflare plans only at the Business or Enterprise plan level.
support.cloudflare.com/hc/en-us/articles/200168706-How-do-I-do-CNAME-setup-
This is possible, however it needs to be set-up via a CloudFlare Partner or you need to be on the Business or Enterprise plan.
stackoverflow.com/a/32764370