0_DrawerContainer.jsx

export default class DrawerContainer extends Component {
  render() {
    return (
      <DrawerLayout
        ref={drawerLayout => (this.drawer = drawerLayout)}
        drawerWidth={300}
        drawerPosition={DrawerLayout.positions.Left}
        //this renders the content of the slide out drawer
        renderNavigationView={() =>
          <Home {...this.props} drawer={this.drawer} />}
      >
        //This is the Home screen which contains the drawer open button 
        <Home {...this.props} drawer={this.drawer} />
      </DrawerLayout>
    )
  }
}

1__Home.jsx

export default class Home extends Component {
  render() {
    return (
      <View style={styles.menu}>
          <TeamMenu {...this.props} />
      </View>
    )
  }
}

2_TeamMenu.jsx

export default class Home extends Component {
  render() {
    return (
      <DrawerButton size={35} {...props} />
    )
  }
}

3_DrawerButton

export default class DrawerButton extends Component {
  render() {
    return (
      <TouchableOpacity
        onPress={() => props.drawer.openDrawer()}
      >
        <Icon name="md-menu" size={props.size} />
      </TouchableOpacity>
    )
  }
}