In the context of the "occupy" protests, I've head a couple of times that you should carry a bandana or cloth soaked in vinegar with you, and in case the police uses tear gas / irritants, you should breath through it, or cover your face with it.

Setting aside legal and moral aspects of preparing for such a situation, say you have a good reason... (And also the fact that is stinks...) Does it work? If so, how?

I'd actually expect the contrary. The vinegar vapors would open up your airways and you would be decapacitated even faster.