How to initialize mysql container when created on Kubernetes?

According to the MySQL Docker image README, the part that is relevant to data initialization on container start-up is to ensure all your initialization files are mount to the container's /docker-entrypoint-initdb.d folder.

You can define your initial data in a ConfigMap, and mount the corresponding volume in your pod like this:

apiVersion: v1
kind: Pod
metadata:
  name: mysql
spec:
  containers:
  - name: mysql
    image: mysql        
    ports:
      - containerPort: 3306
    volumeMounts:
      - name: mysql-initdb
        mountPath: /docker-entrypoint-initdb.d
  volumes:
    - name: mysql-initdb
      configMap:
        name: mysql-initdb-config
---
apiVersion: v1
kind: ConfigMap
metadata:
  name: mysql-initdb-config
data:
  initdb.sql: |
    CREATE TABLE friends (id INT, name VARCHAR(256), age INT, gender VARCHAR(3));
    INSERT INTO friends VALUES (1, 'John Smith', 32, 'm');
    INSERT INTO friends VALUES (2, 'Lilian Worksmith', 29, 'f');
    INSERT INTO friends VALUES (3, 'Michael Rupert', 27, 'm');

First: create persistent volume that contains your SQL scripts

kind: PersistentVolume
apiVersion: v1
metadata:
  name: mysql-initdb-pv-volume
  labels:
    type: local
    app: mysql
spec:
  storageClassName: manual
  capacity:
    storage: 1Mi
  accessModes:
    - ReadOnlyMany
  hostPath:
    path: "/path/to/initdb/sql/scripts"
---
kind: PersistentVolumeClaim
apiVersion: v1
metadata:
  name: mysql-initdb-pv-claim
  labels:
    app: mysql
spec:
  storageClassName: manual
  accessModes:
    - ReadOnlyMany
  resources:
    requests:
      storage: 1Mi

Note: assume that you have your SQL scripts in /path/to/initdb/sql/scripts

Second: mount the volume to /docker-entrypoint-initdb.d

apiVersion: extensions/v1beta1
kind: Deployment
metadata:
  name: mysql
spec:
  replicas: 1
  template:
    metadata:
      labels:
        app: mysql
    spec:
      containers:
        - name: mysql
          image: mysql
          imagePullPolicy: "IfNotPresent"
          ports:
            - containerPort: 3306
          volumeMounts:
            - mountPath: /docker-entrypoint-initdb.d
              name: mysql-initdb
      volumes:
        - name: mysql-initdb
          persistentVolumeClaim:
            claimName: mysql-initdb-pv-claim

That's it.

Note: this applies to PostgreSQL too.