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.


 

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