There are two options.
Replacement
The NS you have been assigned by Cloudflare, for example josh.ns.Cloudflare.com and nina.ns.clodflare.com will be replaced by ns1.domain.org and ns2.domain.org (just examples). You need at least a business plan to do this.
You are maybe required to run the two name servers in different networks. Denpending on the registry.
Delegation
Add NS Records to your dashboard as explained here:
If you are using your provider’s name servers additional A record in this post isn’t needed.
DNS requests for your subdomains will be forwarded to your own DNS servers and you can control them there.