CloudFlare + Sub Domain Only Hosting

We have a setup like this:

Main site is hosted with a different provider.

We have a dedicated server with DreamHost to host our sub domain names like

We don’t host any root domains with DH.
We signed up for the CloudFlare Plus package through the DH panel.

Do we need to do anything on our end to get things going? Or is it taken care of by DH’s end? I don’t have to update the sub domain DNS with our domain provider to point to CloudFlare or anything like that because the root domain’s DNS isn’t hosted with DreamHost, do I?

What is probably most important is whose nameservers are in use for the sub-domains. You really don’t give any clues about that, and it’s one of the most important in explaining your setup

If other than dreamhost, then dreamhost won’t be able to manage the cloudflare DNS.

I believe we just have A records at the domain provider pointing to DreamHost?
Is there a way to have a subdomain point to nameservers themselves? I’m still incredibly new to all of this, so excuse my newbie.