Try these commands:
kubectl proxy --port=8080
You can then access the API with
curl http://localhost:8080/api/
This also allows you to browse the API in your browser. Start minikube using
minikube start --extra-config=apiserver.Features.EnableSwaggerUI=true
then start kubectl proxy, and navigate to http://localhost:8080/swagger-ui/ in your browser.
You can access the Kubernetes API with curl directly using
curl --cacert ~/.minikube/ca.crt --cert ~/.minikube/client.crt --key ~/.minikube/client.key