When your website is on Cloudflare CDN network, adding a domain from your cPanel can be a real pain if you don't know how to go about it. Problems is that the sub-domain will not resolve as the DNS is not mapped yet to the Cloudflare server.

What do you do?
You have to add the sub-domain to Cloudflare manually.

How do I add a subdomain to my website on Cloudflare? The following steps will do it.

a. Log into your Cloudflare account.
b. From the dropdown menu on the top left, select the domain.
c. Select the DNS icon.
d. Select the record type from the record type drop-down on the left-hand side. A sub-domain will either be an A or CNAME record type.

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e. Enter the record name and value.
f. Click Add to finish adding the record.

If you want it powered by Cloudflare, then orange-cloud it.