A:I'm not sure I see the point about the flash—most cameras allow you to turn the flash entirely off—but I do see the point about the dust. (Editorial aside: Are the pictures getting blurry, or is it just you due to absorbing too much Burning Man "atmosphere"?)
Two things you can do. One, find a more dust-proof camera. Two, figure out a way to protect an existing camera.
As for dust-resistance, probably your best bet is the Pentax Optio W90 ($300), a camera that's designed to be dustproof(ish), waterproof (to 20 feet), and shock-resistant. It's also a nice little camera, with a 12.1-megapixel resolution, 5x optical zoom, 720p HD video, and a compact body. The Olympus Stylus Tough 6020 ($300) has similar specs.
Still, given the conditions in which you are working, I think it prudent to do some extra armoring of your camera. In short, by a waterproof (and hence, dustproof) case. This needn't be a big deal. The Aquapac Mini Camera Case fits most compact digitals, as a clear-view lens cover so your pictures look good, and has a clear back panel so you can see your LCD viewfinder. And it costs only $35. The DicaPac Underwater Case is very similar but has a better lens cover (hard polycarbonate). The sizes start at $35. In either case, if the camera cover gets dusty/dirty, you just rinse it off! Pretty convenient. And your camera will return intact, even if you do not.