The DNS server is enabled by default on Plesk and it allows you to use the server a the Primary Name Server. You'll still need setup at least one slave DNS server for use as your secondary name server. Which can be a bit of an hassle.
If you don't want to run a DNS server yourself you can use an external DNS provider to manage your DNS zones. There are some great Plesk Extensions (
Microsoft Azure DNS,
Amazon Route 53,
DigitalOcean DNS) that will sync the DNS zones between Plesk and the DNS provider. This allows you to still manage your DNS settings and records trough Plesk while having to worry about running a DNS server.
I don't believe there is an Extensions to sync your DNS from Plesk to CloudFlare. But you could CloudFlare as your DNS provider if your okay with managing your DNS records manually.
Does this answer your question?