One dustbath a week in the winter alone, should not be causing the dry skin on the ears. Dust baths are used to clean the natural 'extra' lanolin from fur that the chin produces. It also helps remove the oils and dirt we transfer from our skin/hands to them, when handling them. The skin on their ears, their nose and pads of their feet is not as protected as the skin on the rest of the body that is covered with fur. The exposed skin is much more sensitive to the environment and everything in it (including dust mites, fumes from cologne, allergents, new detergents being used on clothing or surfaces, their bedding and the air itself), any or all of which can cause a problem.
In the wintertime, most of us keep the windows closed tight, keeping out the cold, but also keeping out the natural moisture that would be in the air.
The heating systems also tend to dry the air inside the home even more.
Airing out the house for about an hour, at least once a week, is not only good for your chin, but good for you, too. Most homes have a lower quality of air inside the house, in the wintertime, than the air quality that is outside.
When your chin is showing dry skin, you might want to get it checked by the vet to make sure it is not something other than just dry skin.
You might consider putting some moisture in the air (a small can or container of water near the heat source) in the room where the chinchilla stays.
A chinchilla can have problems with high humidity, but there are also problems that can be caused by the humidity being to low, also.
Normally, I would not suggest the use of a humidifier, but, you might want to check with your vet about that.
A chinchilla does best when the humidity is about 30% to 35%, I think. I'm going to check with a couple of people about that and will post what they tell me.
Jo Ann