kube-ui is deployed as a cluster add-on. To find its apiserver proxy URL,
$ kubectl cluster-info | grep "KubeUI" KubeUI is running at https://184.108.40.206/api/v1/proxy/namespaces/kube-system/services/kube-ui
if this command does not find the URL, try the steps here.
The above proxy URL is an access to the kube-ui service provided by the apiserver. To access it, you still need to authenticate to the apiserver.
kubectl proxy can handle the authentication.
$ kubectl proxy --port=8001 Starting to serve on localhost:8001
Now you can access the kube-ui service on your local workstation at http://localhost:8001/api/v1/proxy/namespaces/kube-system/services/kube-ui