Coal flue gases are very corrosive to steel, stainless included, but any light gauge non-stainless flue pipe will rust out after a season or two collapsing and causing a potentially dangerous situation. If your brick chimney is sound, and you have no wood-burning appliance attatched to the same flue, any steel liner is unnecessary and will likely lead to a more dangerous situation in a short amount of time. A liner gives an extra barrier to creosote penetration of the mortar joints and adds another layer of protection to contain a chimney fire - this does not apply to coal as coal produces no flammable or tarry creosote, only powdery soot and flyash.
The stoker is somewhat innefficient as manufactured because it has a small heat exchanger for the btu output. To solve this a much larger fan to blow air over the heat exchanger faster to remove more heat is best, such as a large "furnace blower" or squirrel cage type fan fitted where the small heat exchanger fan is located from the factory. Even with a larger fan fitted to the main heat exchanger, your stack temps (burning decent btu coal and even on the lowest feed rate) will exceed 450ºF. To solve this problem, I highly reccomend a "magic heat" type flue heat exchanger be located on the flue shortly after it exits the stove and hardwired into the fan/limit control switch on the appliance (don't use the "magic heat's" built in thermostat to control the flue heat exchanger fan if you choose to purchase one).