With Google "Private IP" the cloud proxy is now irrelevant!

I found a solution.

Deploy the proxy with the yml below, and expose the deployment as a service. Most importantly, make the proxy listen on 0.0.0.0, instead of default 127.0.0.1. All the secrets as per the Google Cloud sql documentation

apiVersion: extensions/v1beta1
kind: Deployment
metadata:
  name: mysql
spec:
  replicas: 1
  template:
    metadata:
      name: mysql
      labels:
        name: mysql
    spec:
      containers:
         - image: b.gcr.io/cloudsql-docker/gce-proxy:1.05
           name: cloudsql-proxy
           command: ["/cloud_sql_proxy", "--dir=/cloudsql",
                     "-instances=MYSQL:ZONE:DATABASE_INSTANCE=tcp:0.0.0.0:3306",
                     "-credential_file=/secrets/cloudsql/credentials.json"]
           volumeMounts:
             - name: cloudsql-oauth-credentials
               mountPath: /secrets/cloudsql
               readOnly: true
             - name: ssl-certs
               mountPath: /etc/ssl/certs
           ports:
             - containerPort: 3306
               name: mysql
      volumes:
        - name: cloudsql-oauth-credentials
          secret:
            secretName: cloudsql-oauth-credentials
        - name: ssl-certs
          hostPath:
            path: /etc/ssl/certs

The solution is slightly more expensive than having the proxy in the same deployment as the client software, since there is an extra TCP connection.

However there are many benefits:

• Much simpler and doesn't require modifying existing K8S deployment files
• Allows switching the implementation to a MySQL Docker container or using the Google Cloud SQL proxy without any modifications to the client configuration.

You can create a deployment and a service to expose the cloudsql proxy to other pods like so:

apiVersion: v1
kind: Service
metadata:
  name: cloudsqlproxy
spec:
  ports:
  - port: 3306
    targetPort: database-port
  selector:
    app: cloudsqlproxy
---
apiVersion: extensions/v1beta1
kind: Deployment
metadata:
  name: cloudsqlproxy
spec:
  template:
    metadata:
      labels:
        app: cloudsqlproxy
    spec:
      volumes:
      - name: service-account-token
        secret:
          secretName: service-account-token
      containers:
      - name: cloudsql-proxy
        image: gcr.io/cloudsql-docker/gce-proxy:1.11
        imagePullPolicy: Always
        command:
        - /cloud_sql_proxy
        - -instances=<project>:<cloudsqlinstance>=tcp:0.0.0.0:3306
        - -credential_file=/secrets/cloudsql/credentials.json
        ports:
        - name: database-port
          containerPort: 3306
        volumeMounts:
        - name: service-account-token
          mountPath: /secrets/cloudsql
          readOnly: true

So within any of your pods, the database your MYSQL_HOST:MYSQL_PORT will be cloudsqlproxy:3306

For multiple databases through the same proxy, you'd have the same deployment structure for the proxy, except that you will now expose 2 ports from the pod, like so:

apiVersion: extensions/v1beta1
...
spec:
  template:
    ...
    spec:
      volumes:
      ...
      containers:
      - name: cloudsql-proxy
        ...
        ports:
        - name: database-port1
          containerPort: 3306
        - name: database-port2
          containerPort: 3307
        ...

Then you'd create 2 services to for discovery on those ports like so:

apiVersion: v1
kind: Service
metadata:
  name: cloudsqlproxy-db1
spec:
  ports:
  - port: 3306
    targetPort: database-port1
  selector:
    app: cloudsqlproxy
---
apiVersion: v1
kind: Service
metadata:
  name: cloudsqlproxy-db2
spec:
  ports:
  - port: 3306
    targetPort: database-port2
  selector:
    app: cloudsqlproxy

So, with both services set to port 3306, you can connect to each database on that port:

mysql --host=cloudsqlproxy-db1 --port=3306 ...
mysql --host=cloudsqlproxy-db2 --port=3306 ...

Reference: https://github.com/GoogleCloudPlatform/cloudsql-proxy/blob/master/Kubernetes.md