That is a deep level of sub-domain, moreover if I understand correctly you are using custom domain with wpengine and want Cloudflare over it?
Have you checked out here:
Is it added as a A or a CNAME record to the domain DNS at Cloudflare dashboard?
Moreover, to use a sub.subdomain.wpengine.com SSL certificate, I am afraid you would need to purchase Cloudflare Dedicated SSL with Custom Hostname for $10/month. Moreover, you need this since Cloudflare Universal SSL only provide for *.subdomain.wpengine.com level.
could be I am wrong …
More about dedicated SSL certificates here:
Nevertheless, if this error appears in your browser this is a strong indicator that the hostname is not present on the SSL certificate located at Cloudflare edge.
If you require mutli-level sub-domain support you will either need to purchase this feature or upgrade your Plan to Business so that you can upload a Custom Certificate (hopefully if you have one at your host/origin which already supports sub.subdomain.wpengine.com.
I suppose yes due to (I hope it covers the CNAME because you use wpengine.com):
You can include up to 100 hostnames or wildcard hostnames on a single certificate and can include hostnames for other domains within the same Cloudflare account. You can also add support for multi-level subdomains such as .test.dev.www.example.com .