If you just use Cloudflare as a registrar, then they can't see what resolution happens on your servers.
If you delegate a subdomain through Cloudflare to your own DNS servers, from what I remember from the animal book, the recursive server should ask Cloudflare for the address of the machine to which the delegation has been made (yours), and while any further resolutions would be answered by your machine, Cloudflare would at very least know of every query to that subdomain.
If you delegate a subdomain and have subdomains under that subdomain, then Cloudflare would only see resolutions to that subdomain and not to the sub-subdomains.
In other words, for most things, they'd have full insight.
If you delegate a subdomain through Cloudflare to your own DNS servers, from what I remember from the animal book, the recursive server should ask Cloudflare for the address of the machine to which the delegation has been made (yours), and while any further resolutions would be answered by your machine, Cloudflare would at very least know of every query to that subdomain.
If you delegate a subdomain and have subdomains under that subdomain, then Cloudflare would only see resolutions to that subdomain and not to the sub-subdomains.
In other words, for most things, they'd have full insight.