Use the following code to add the Woocommerce order ID to a field in a Formidable form after the order is placed in Woocommerce. You will need to add a hidden field to your form. After a checkout is completed, the order ID will be added to the hidden field. Replace 25 with the ID of your form and replace 123 with the ID of the hidden field.

add_action( 'woocommerce_new_order_item', 'add_order_id_to_entry', 10, 3 );
function add_order_id_to_entry( $item_id, $cart_item, $order_id ) {

  // check if there's form data to process
  if ( empty( $cart_item->legacy_values['_formidable_form_data'] ) ) {
    return;
  }

  // get form entry
  $entry = FrmEntry::getOne( $cart_item->legacy_values['_formidable_form_data'] );
  if ( $entry && $entry->form_id == 25 ) {
    $field_id = 123;
    $added = FrmEntryMeta::add_entry_meta( $entry->id, $field_id, null, $order_id );
    if ( ! $added ) {
      FrmEntryMeta::update_entry_meta( $entry->id, $field_id, null, $order_id );
    }
  }
}

An extension of the 'Add Order ID to Entry' customization

add_action( 'woocommerce_new_order_item', 'save_entry_data_with_order', 10, 3 );
function save_entry_data_with_order( $item_id, $cart_item, $order_id ) {

// check if there's form data to process
if ( empty( $cart_item->legacy_values['_formidable_form_data'] ) ) {
return;
}

// get form entry
$entry = FrmEntry::getOne( $cart_item->legacy_values['_formidable_form_data'] );
if ( $entry ) {
global $wpdb;
// Order ID Field - Change 'woo order id' text to name of order id field in your form
$field_id = $wpdb->get_var ( $wpdb->prepare( "SELECT id FROM {$wpdb->prefix}frm_fields where name = 'woo order id' and form_id = %d ", $entry->form_id) );
$added = FrmEntryMeta::add_entry_meta( $entry->id, $field_id, null, $order_id );
if ( ! $added ) {
FrmEntryMeta::update_entry_meta( $entry->id, $field_id, null, $order_id );
}

// code below here is to save any custom fields to the WooCommerce Order Meta table to allow for easier use when combining with orders
// note that you can comment out any or all below if you do not want to save entry data with the order meta
// you will need to change the Name of the field in each query to the name of your field you want saved to the order
// be sure to change '_custom_key' text to whatever you would like your keyname to be in the order meta

$field_id = $wpdb->get_var ( $wpdb->prepare( "SELECT id FROM {$wpdb->prefix}frm_fields where name = 'Additional Person Name' and form_id = %d ", $entry->form_id) );
$meta_value = FrmEntryMeta::get_meta_value( $entry, $field_id );
if($meta_value === NULL) {$meta_value='';}
update_metadata( 'post', $order_id, '_custom_key_1', $meta_value );

// Additional Person Email Field
$field_id = $wpdb->get_var ( $wpdb->prepare( "SELECT id FROM {$wpdb->prefix}frm_fields where name = 'Additional Person Email' and form_id = %d ", $entry->form_id) );
$meta_value = FrmEntryMeta::get_meta_value( $entry, $field_id );
if($meta_value === NULL) {$meta_value='';}
update_metadata( 'post', $order_id, '_custom_key_2', $meta_value );

// Additional Person Phone Number Field
$field_id = $wpdb->get_var ( $wpdb->prepare( "SELECT id FROM {$wpdb->prefix}frm_fields where name = 'Additional Person Phone Number' and form_id = %d ", $entry->form_id) );
$meta_value = FrmEntryMeta::get_meta_value( $entry, $field_id );
if($meta_value === NULL) {$meta_value='';}
update_metadata( 'post', $order_id, '_custom_key_3', $meta_value );

// Total Field
$field_id = $wpdb->get_var ( $wpdb->prepare( "SELECT id FROM {$wpdb->prefix}frm_fields where name = 'Total' and form_id = %d ", $entry->form_id) );
$meta_value = FrmEntryMeta::get_meta_value( $entry, $field_id );
if($meta_value === NULL) {$meta_value='';}
update_metadata( 'post', $order_id, '_custom_key_4', $meta_value );
}
}