In 2012, there was a fairly well stocked shop in the mall in Puerto Montt, and a less-well-stocked shop in Puerto Varas. I think for a stove and sleeping bag the shops in Puerto Varas will be fine. Be warned that prices are steep everywhere, in my experience.
Edit to add: I think the Puerto Varas shop was called Tierra and was in the main shopping square. I can't remember the Puerto Montt shop's name, but it was in the mall. Puerto Montt is also pretty big and I'm sure there are others.