How do I access this Kubernetes service via kubectl proxy?

With Kubernetes 1.10 the proxy URL should be slighly different, like this:

http://localhost:8080/api/v1/namespaces/default/services/SERVICE-NAME:PORT-NAME/proxy/ 

Ref: https://kubernetes.io/docs/tasks/access-application-cluster/access-cluster/#manually-constructing-apiserver-proxy-urls

As Michael says, quite possibly your labels or namespaces are mismatching. However in addition to that, keep in mind that even when you fix the endpoint, the url you're after (http://localhost:8001/api/v1/proxy/namespaces/monitoring/services/grafana) might not work correctly.

Depending on your root_url and/or static_root_path grafana configuration settings, when trying to login you might get grafana trying to POST to http://localhost:8001/login and get a 404.

Try using kubectl port-forward instead:

kubectl -n monitoring port-forward [grafana-pod-name] 3000

then access grafana via http://localhost:3000/

https://kubernetes.io/docs/tasks/access-application-cluster/port-forward-access-application-cluster/

The issue is that Grafana's port is named web, and as a result one needs to append :web to the kubectl proxy URL: http://localhost:8001/api/v1/proxy/namespaces/monitoring/services/grafana:web.

An alternative, is to instead not name the Grafana port, because then you don't have to append :web to the kubectl proxy URL for the service: http://localhost:8001/api/v1/proxy/namespaces/monitoring/services/grafana:web. I went with this option in the end since it's easier.