Gravity Forms doesn't offer a function to export a date field as a UNIX timestamp. This function will find all exported dates in a GF submission & convert it to UNIX, and then update the postmeta to the proper format - as is, it will ONLY work if you're using the Gravity Forms + Custom Post Types plugin to create or edit a post

gf-convert-to-timestamp.php

add_action( 'gform_after_submission', '_convert_date_to_timestamp', 10, 2 ); // Extend

function _convert_date_to_timestamp( $entry, $form ) {

	date_default_timezone_set ( "America/Denver" );

	// Make sure that we're submitting a post before running the code
	if ( $entry['post_id'] ){
		foreach ( $entry as $key => $value ){

			if ( preg_match( '/(\d{4})-(\d{2})-(\d{2})/', $value ) ) {

				// Make sure that we're not overriding  the date_created field
				if ( $key != 'date_created' ){

					// Get the $form fields array id so that we can recover our custom field name
					foreach ( $form[fields] as $fields_key => $fields_value ){

						if ( $fields_value['id'] == $key ){

							$field_id = $fields_key;

						} // endif

					} // endforeach

					$cpt_name = $form[fields][$field_id][postCustomFieldName];
					$reformatted_date = date( 'U', strtotime( $value ) );

					update_post_meta( $entry['post_id'], $cpt_name, $reformatted_date );

					// return to format - $date = date('m-d-Y', $Udate);

				}
			}
		}
	}
}