Is it a "Duck" material with a thin layer of rubber sandwiched between two layer of fabric, in which case heat could cause damage and may mean dry cleaning is out
Hi John..It might we worth trying one of the "dry" carpet cleaners like Vanish Gold Carpet Cleaner...comes as a spray on foam that you vacuum off when its dry and lifts off dirt.
If you mist spray the fabric with water to damp it ,spray on a light covering of foam and work in to fabric with soft microfiber cloth or VERY soft short bristle ( finger nail cleaning ) brush and then let it dry naturally and vacuum over. Obviously do a small test piece to check colour fastness and chemical compatibility first .