You have seen the basics about kubectl proxy and apiserver proxy. This guide shows how to use them together to access a service(kube-ui) running on the Kubernetes cluster from your workstation.
Getting the apiserver proxy URL of kube-ui
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://173.255.119.104/api/v1/proxy/namespaces/kube-system/services/kube-ui
if this command does not find the URL, try the steps here.
Connecting to the kube-ui service from your local workstation
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