A steel brush will scratch a stainless steel chimney....use a poly brush! A poly brush will not give you the friction that a steel brush will either and move up and down the pipe easier. Really, creosote does not stick to the smooth interior of a stainless steel chimney all that much. Creosote will stick to a scratched stainless steel chimney, tho.....so don't scratch it with a steel brush.
I'm willing to bet that some of the negative posts in this thread are from people having a clay flue chimney or from those using a steel brush in a stainless steel chimney.
Use a nylon rod, a poly brush, a ball on the downward end of the brush, and you will have no problem cleaning a stainless steel chimney.