A cloudbuild that works for me with private packages

app.yaml

env: flex
runtime: go1.12
main: cmd/some-service-name/main.go

cloudbuild.yaml

substitutions:
  _APP: github.com/automaticalldramatic/some-app-name

options:
  volumes:
    - name: 'ssh'
      path: /root/.ssh

steps:
  - id: decrypt keys
    name: 'gcr.io/cloud-builders/gcloud'
    args:
      - kms
      - decrypt
      - --ciphertext-file=gcp_id_rsa.enc
      - --plaintext-file=/root/.ssh/id_rsa
      - --location=global
      - --keyring=automaticalldramatic-keyring
      - --key=github-key

  # Set up git with key and domain.
  - id: setup ssh
    name: 'gcr.io/cloud-builders/git'
    entrypoint: 'bash'
    args:
      - '-c'
      - |
        chmod 600 /root/.ssh/id_rsa
        cat <<EOF >/root/.ssh/config
        Hostname github.com
        IdentityFile /root/.ssh/id_rsa
        EOF
        mv known_hosts /root/.ssh/known_hosts
        ls -al /workspace

  - name: 'gcr.io/cloud-builders/git'
    entrypoint: 'git'
    args:
      - config
      - --global
      - --add
      - url.git@github.com:.insteadOf
      - https://github.com/

  - name: mirror.gcr.io/library/golang
    args:
      - go
      - get
      - "google.golang.org/appengine"
    env:
      - GO111MODULE=on
      - GOPATH=/go
      - PROJECT_ROOT="/go/src/${_APP}"
    volumes:
      - name: go-modules
        path: /go

  # Build the module.
  - id: build the module
    name: mirror.gcr.io/library/golang
    args: ['go', 'get', '-u', './...']
    env:
      - GO111MODULE=on
      - GOPATH=/go
      - PROJECT_ROOT="/go/src/${_APP}"
    volumes:
      - name: go-modules
        path: /go

  # Copy the pkg/mod to /src
  - id: copy go pkg mods
    name: mirror.gcr.io/library/golang
    entrypoint: 'bash'
    args:
      - '-c'
      - |
        cp -R /go/pkg/mod/* /go/src/
    volumes:
      - name: go-modules
        path: /go

  - id: deploy app
    name: 'gcr.io/cloud-builders/gcloud'
    args:
    - app
    - deploy
#    dir: "/go/src/${_APP}"
    env:
      - GO111MODULE=on
      - GOPATH=/go
      - PROJECT_ROOT="/go/src/${_APP}"
#    volumes:
#      - name: go-modules
#        path: /go

service
  |
  |__cmd
  |  |_main.go
  |
  |_ app.yaml
  |_ cloudbuild.yaml
  |_ service.go
  |_ someHelper.go