The actual setup depends on your cloud provider and what they recommend for multi-Kubernetes setups. (not sure if Azure supports providing a routable subnet to the AKS cluster)
I guess this leaves DNS only but I have a vague feeling with it too a not a good one because once in a while there is something weird going on with the DNS between the cluster, I don’t have a concrete example of that but the weird feeling that I would run into issues.
DNS will only be used for the initial connection to the cluster, after that the clients will make use of the IP addresses of the Pods. So DNS is not in the critical path. For completeness there was an issue with DNS reported here: FDB regular recovery with operator - #10 by jlemaes