Generally, a subdomain does not work on Cloudflare because it hasn't been added it to your zone file for the domain.
To add a subdomain, review How do I add a subdomain.
Your subdomain DNS record should be either an A record (you need the IP address to point to) or a CNAME (you need another subdomain for it to point to).
- A record - your blog points to a server IP address
- CNAME record - your blog is an alias for another domain or subdomain