Adding birthday field to Mailchimp

Hi!
I’m trying to add a custom birthday field to my checkout page from Woocommerce, and at the same time I’m trying to add this data into Mailchimp so I can make a birthday automation.

I did manage to show an extra field in my checkout page where I can add my birthday. However, when placing an order I find the label ‘Geboortedatum’ (dutch for Birthday) in my order information in Woocommerce, however, only the label and not the birthday itself. Besides that I don’t see any information back in Mailchimp audience contact (I did synchronize information about the order, so I see my order and order amount etc in Mailchimp, just nothing about the birthday).

This is the code I used, I have no idea what is going wrong.. Hope someone can help me!

// Hook in add date of birth in checkout field
add_filter( 'woocommerce_checkout_fields' , 'custom_override_checkout_fields' );
// Our hooked in function – $fields is passed via the filter!
function custom_override_checkout_fields( $fields ) {
     $fields['billing']['billing_date_of_birth'] = array(
		 'type'		=> 'date',
        'label'     => __('Geboortedatum'.'<br>'.'<small>Laat je verassen op je verjaardag!</small>', 'woocommerce'),
    'placeholder'   => _x('Geboortedatum', 'placeholder', 'woocommerce'),
    'required'  => false,
    'class'     => array('form-row-wide'),
    'clear'     => true
     );
     return $fields;
}
/**
 * Display field value on the order edit page
 */
add_action( 'woocommerce_admin_order_data_after_billing_address', 'my_custom_checkout_field_display_admin_order_meta', 10, 1 );
function my_custom_checkout_field_display_admin_order_meta($order){
    echo '<p><strong>'.__('Geboortedatum').':</strong> ' . get_post_meta( $order->get_id(), 'date_of_birth', true ) . '</p>';
}



function mailchimp_custom_order_merge_tags($merge_tags, $order) {

    $birthday = get_post_meta( $order->getId(), 'date_of_birth', true );
    /// add whatever you want to the merge tags
    $merge_tags['MMERGE3'] = $birthday;

    return $merge_tags;
}

add_filter('mailchimp_get_ecommerce_merge_tags', 'mailchimp_custom_order_merge_tags', 10, 2);