There is a lot of documentation but not specific about Dockerfiles (or I missed it).
My app.yaml file:
runtime: custom
env: flex
env_variables:
MYSQL_DSN: mysql:unix_socket=/cloudsql/project-name:europe-west1:test001;dbname=db001
MYSQL_USER: root
MYSQL_PASSWORD: 'qwerty'
My Dockerfile:
FROM ubuntu:16.04
ARG dbuser
ENV dbuser ${MYSQL_USER}
ARG dbpass
ENV dbpass ${MYSQL_PASSWORD}
ARG dbhost
ENV dbhost ${MYSQL_DSN}
RUN apt-get update
RUN apt-get install mysql-client
RUN mysql -h ${dbhost} -u ${dbuser} -p${dbpass} -e "CREATE DATABASE 'test';"
Documentation followed: