This is not plan related, no Cloudflare-registered domain can use nameservers other than the assigned ones. You will need to configure the required DNS entries within your Cloudflare DNS panel.
As I understand it, when a host asks you to change your domains NS record to reflect their nameservers, the host will be managing the DNS.
In this case, with Digital Ocean, I can’t change the NS record in Cloudflare to reflect what Digital Ocean is asking as listed in my first post (ns1, ns2, ns3).
How do I go about linking my server to Digital Ocean since I can’t change the name servers?
Digital Ocean is a self-service VPS provider and they would not be managing your DNS even if you were using their nameservers. You would still be responsible for creating the same DNS records in your zone on Digital Ocean nameservers as you will using Cloudflare nameservers.
If you need DNS records for hostnames that you run on Digital Ocean droplets, you will need to find the IP address of the resource in your Digital Ocean dashboard.