Hamsters do like to groom themselves quite a bit and often groom immediately after handling to get rid of your scent really!!!
Is he scratching at one place or just all over?
It is possible for hamster to get parasites such as mites, lice and fungal skin infections. They can catch them from other animals, wild and pet, or from bedding which has carried it to them. If you use hay as bedding they can get mites from this. They can also develop allergies to sawdust and household sprays, disinfectants etc which can cause itching.
Part the fur and see if you can see any redness, scabs, dry skin or fur loss. If you can a trip to the vet is needed to have the cause identified and treated. If you think it is an allergy change his bedding to plain white toilet roll ripped up and maybe try a paper based substrate such as carefresh rather than wood shavings. As hamsters get older they are prone to dry skin and fur loss and you may want to supplement the diet with some porridge such as ready brek and a yeast tablet crushed over his food. Also a drop of cod-liver oil can help.
Hamsters should never have chinchilla DUST as it can be dangerous to them. They can have Chinchilla SAND but it must be sand (we use the Charlie chinchilla) and you can put it in a shallow dish or hamster potty. Most will roll then use it as a potty.
I hope he is just normal grooming as they are clean little critters. Keep us posted