What product is the best to use to clean speaker cloth?

You have to be careful when you clean your speakers because some of the parts are delicate and you do not want to damage your speakers. You should clean your speakers periodically so they will give you the best sound possible.
If the grille is a fabric one you can vacuum it to get rid of the dust. I would try the upholstery brush on a vacuum cleaner. If the grille is soiled or stained gently rinse with warm water and lay them out to dry before putting them back on. You can use one of the "Dry Clean" aerosols available at Auto Stores, like Blue Coral Dri-Clean.