TL;DR
dnsutilsをインストールして、nslookupを実行するだけです。
https://kubernetes.io/docs/tasks/administer-cluster/dns-debugging-resolution/
dnsutilsのインストール
$ kubectl apply -f https://k8s.io/examples/admin/dns/dnsutils.yaml
pod/dnsutils created
$ kubectl get pods dnsutils
NAME READY STATUS RESTARTS AGE
dnsutils 1/1 Running 0 20s
nslookupでDNSに問い合わせる
$ kubectl exec -i -t dnsutils -- nslookup prometheus-server.istio-system.svc.cluster.local
Server: 10.96.0.10
Address: 10.96.0.10#53
Name: prometheus-server.istio-system.svc.cluster.local
Address: 10.97.230.212
$ kubectl exec -i -t dnsutils -- nslookup flagger-loadtester.test
Server: 10.96.0.10
Address: 10.96.0.10#53
** server can't find flagger-loadtester.test: NXDOMAIN
command terminated with exit code 1