We are a Commission Scolaire du Québec and we would like to be able to manage our domain.gouv.qc.ca subdomain on our Cloudflare account. Obviously we don’t have access to the parent domain. They added our Cloudflare NS. However, we still can’t add our subdomain …
That’s the main point. You cannot add sub-domain to your Cloudflare account.
Firstly, you have to add the naked domain like domain.com.
Therefore, you create an A record for sub.domain.com or sub.sub.domain.com.
Nevertheless, for that “deep” sub-domains with Xth and so on level, I am afraid you would also have some issues in terms of the SSL certificate as far as below article explains more in detail:
Meaning, they are managing their DNS records by their Cloudflare account to which, you as obviously, again, do not have the access, right?
Could you ask them to add your e-mail / account under their main Cloudflare account, so you could, at least, manage the needed?
See below article for more information about Multiple-user accounts on Cloudflare:
Otherwise, you could ask them to add a new DNS record for that sub.domain.comsub.sub.domain.com, therefore depending which level that sub-domain is, I am afraid they would have to purchase an SSL certificate using Advanced Certificate Manager from below link in case of cloud (Proxy mode for that sub or sub.sub domain):
Nevertheless, if you have an SSL certificate on your origin host / server which covers that sub-domain or sub.sub-domain, they could set it to (DNS-only) - but in that case, you lose all the benefits from Cloudflare and you actually do not need Cloudflare in that terms as well (from my understanding and my point of a view).
Could be I am wrong about something.
Kindly and patiently, wait for another reply if so.