Fur chewing looks like someone went at a chinchilla with scissors. If it is fungus, which causes fur loss, you will find bald spots. If it is normal shedding, it will be wisps of dead fur, which you may find are easy to swipe off with your hand or by gently grooming the chinchilla with a comb. Fur chewing can also cause skin to be exposed. If it is that bad, you will see still the tips of the fur coming through the skin, still. Fungus is when it is as bald as bald can be. No tips of fur at all and smooth. Sometimes there can be discoloration of the skin, flaking of the skin or in some fungus cases, even cracked and bleeding skin.
If you are not seeing any patches, it is just likely his normal shedding. As chins get older, and bigger, they shed more too.