With DirectAdmin you can utilize the builtin Multi-Server function to sync DNS records to additional servers.
You can install this free plugin DirectSlave, to add additional edge DNS servers without additional DirectAdmin licenses.
Single DirectAdmin Server with multiple Edge Servers
To use this setup, simply input one provisioning server (The main DirectAdmin server) under your WHMCS. For the Nameservers setup, you would use the hostnames that are pointing to your Edge servers, and not your DirectAdmin server.
For example, if you have 4 edge servers, then use each one of the hostname to point to these 4 edge servers. ns1/ns2/ns3/ns4.yourdomain.com, each pointing to different Edge server's IP address.
Single DirectAdmin Server with multiple Edge Servers with round-robin
To use this setup, simply input one provisioning server (The main DirectAdmin server) under your WHMCS. For the Nameservers setup, you would use the hostnames that are pointing to your Edge servers, and not your DirectAdmin server.
For simplicity sake, you have 4 edge servers; Edge1, Edge2, Edge3, Edge4. and two nameserver prefixes ns1/ns2.yourdomain.com.
For ns1, you would setup round-robin DNS entry to Edge1 and Edge 2. And for ns2, you would setup round-robin DNS entry to Edge 3, Edge 4.
With this setup, you would only use enter ns1 and ns2 in the Nameservers setup.