I think a Linteater is just the ticket for cleaning that vent. I had one at my old house, used it for the dryer vent and my pellet stove vent. It worked great.
My new house only has like 2' of dryer vent as the dryer is right up against the outside wall, so I ended up giving the Linteater to my father.--
So put me on a highway, and show me a sign.
And take it to the limit one more time...