How do I force Kubernetes CoreDNS to reload its Config Map after a change?

One way to apply Configmap changes would be to redeploy CoreDNS pods:

kubectl rollout restart -n kube-system deployment/coredns

You can edit it in command line:

kubectl edit cm coredns -n kube-system

Save it and exit, which should reload it.

If it will not reload, as Emruz Hossain advised delete coredns:

kubectl get pods -n kube-system -oname |grep coredns |xargs kubectl delete -n kube-system