Most backup plugins will not backup the entire folder structure of a Flywheel site – they are unable to access the ‘wp-content’ folder. One method is to use the https://duplicator.com plugin as this does seem to capture everything.
Once the site has been restored, you may need to edit the .htaccess file, the wp-config.php file and replace the wp-settings.php file to remove the Flywheel settings and turn it back into a ‘normal’ WordPress site.