I'm not particularly familiar with Formidable Forms, I assume you can create posts with them, and include fields that will generate custom fields for the submitted post, but you'd have to refer to their documentation for clarification about that.
Assuming it can, then—yes—it should just be a matter of telling it that the field key should be something like 'wpcf-priority' for a field registered with Types with a slug of 'priority'.
The checkboxes field is a no-no. It's the most complex kind of field available in Types.
If your Formidable Form had a checkboxes field (or similar field type that allowed you to select multiple options) then one option would be to add some code to process the form submission (again, you'd need to consult the Formidable documentation about that), and you could try to update the options of a Types checkboxes field using an unofficial API function I'll share below. Some programming is unavoidable, though, if you want this.
/**
* Unofficial API function to check/uncheck checkboxes options
*
* @param int $post_id
* @param string $field // slug of checkboxes field
* @param string $option // title of checkbox option to manipulate
* @param string $action : 'check' | 'uncheck' | 'value' (default, returns current value)
*
* Important: assumes recommended checkboxes setting of save nothing to database when unchecked
*/
function ts_checkboxes( $post_id, $field, $option, $action = 'value' ){
if ( isset($post_id) && isset($field) && isset($option) ){
$field_settings = types_get_field( $field );
$field_options = $field_settings['data']['options'];
// Locate the option key
$key = array_search( $option, array_column( $field_options, 'title' ) );
$keys = array_keys( $field_options );
$option_key = $keys[$key];
// Get the current post meta value
$meta = get_post_meta( $post_id, 'wpcf-'.$field, true );
if ( !is_array($meta) ){
$meta = [];
}
// If action = 'value' just return the value
if ( $action == 'value' && isset( $meta[$option_key] ) ){
return $meta[$option_key][0];
} else {
// Remove the existing key if it exists (i.e. uncheck)
// because recommended setting is to save nothing when unchecked
// if ( is_array($meta) ) {
unset( $meta[$option_key] );
// } else {
// $meta = [];
// }
// If $checked == true then add back the key + value
if ( $action == 'check' ){
$meta[$option_key] = array($field_options[$option_key]['set_value']);
}
update_post_meta( $post_id, 'wpcf-'.$field, $meta );
}
}
}
Examples of how you would use the above function:
// 1. Get the value of the option "Second checkbox" of a checkboxes field "Available options" from the current post:
global $post;
$value = ts_checkboxes( $post->ID, 'available-options', 'Second checkbox' );
// 2. set the same option as checked
global $post;
ts_checkboxes( $post->ID, 'available-options', 'Second checkbox', 'check' );
// 3. set the same option as unchecked
global $post;
ts_checkboxes( $post->ID, 'available-options', 'Second checkbox', 'uncheck' );