I use Cloudflare to provide DNS and loadbalancing for my site (eg mysite (dot) com)
My site provides a service used by an external organisation. They have their own domain infrastructure (eg alloforg (dot) com).
They want to have my service as a subdomain of their DNS infrastructure (eg myservice (dot) alloforg (dot) com). I can only provide an IP address or CNAME to go into the customers DNS infrastructure, but it is not hosted on Cloudflare and this will not change.
Should I just use CNAME functionality to point myservice.alloforg to alloforg.mysite or would I be better pointing to a Cloudflare IP address and if so, which one?
My site can handle the different host header / SNI and this is desirable. I just need to find a way to get traffic from myservice.alloforg.com to the load balancer in Cloudflare so traffic is distributed across my servers and protected in case of a single site failure etc.