Why the correct flue is necessary for heating firewood?
Because when burning firewood big heat is allocated and, as a result, the flue is heated. If to put a flue made of  inappropriate stainless steel,  the flue will burn through. The pipe with the high content of carbon will be made red-hot. Of course  it is possible to argue differently:  you go to a market  and  buy a thinner and cheaper flue  , with a discount card.

But in all that concerns fire,  it is reasonable to observe all precautionary measures as much as possible! It is better excessive care, than excessive risk. This is misfortune when baths burn;  it is the tragedy if people perish. But what does it mean?  Not to build a bath? Of course, to build! The correct flue is necessary not as a safety cushion, but as serviceable brakes in the car.
If to put the correct flue, the problem of removal of a smoke will leave forever. For the correct flue its thickness has to be at least 1 mm. AISI 321 stainless steel with the titan. Not to put at all a flue which is attracted by a magnet (ferritic stainless steel) 
it is impossible to use such thin internal pipe which can be crumpled by a hand. You don't build a house of a cardboard. Therefore don't put in it a flue of a foil! 
Thickness of the used basalt heater is 35 mm. In the table the internal diameter of a pipe and the price in hryvnias is specified. For example, for a pipe with a diameter of sleeve of 100 mm an external diameter of cover is 170 mm.You can look at appearance of an element, having clicked on the corresponding position in a price list.

Таблица: 1. A  nonheat-insulated flue (bare, for гильзовки of brick channels) thickness of metal is 1 mm (AISI  321 with titan)
A diameter is in мм., price is according to internal diameter in hryvnias.
Отвод=challenge, тройник=tee, шибер=flap

2.1  A  metal flue of a 1 mm thickness (AISI  321 with titan) heat-insulated in casing  made of mirror stainless steel of 0,5 мм thickness.

2.2  A  metal flue of a 1 mm thickness (AISI  321 with titan) heat-insulated in casing  made of  galvanized steel of 0,5 мм thickness