Yes, chinchillas can safely eat plain rice cakes.
However there are times that a chinchilla will not eat a rice cake if they do not like the taste.
As you would imagine a rice cake is made out of rice. It has fibre content and is low in calories and fat.
Additionally the good thing about rice cakes is that they supply minerals and vitamins to your chinchilla.
Rice cakes are considered a nutritious food and helpful for red blood cells.