The general cause of a subdomain on Cloudflare not working on a site is that you haven't added it in your zone file for the domain.
You can add your subdomain by following the steps below:
1) Log into your Cloudflare account. 2) From the drop-down menu on the top left, select the domain. 3) Select the DNS icon. 4) Select the record type from the record type drop-down on the left-hand side. A subdomain will either be an A or CNAME record type. 5) Enter the record name and value. 6) Click Add to finish adding the record. 7) Click Add to finish adding the record.