The smoking just may have save you from burning down the house.
For a wood stove you can only connect it to a flu that is designed for wood stoves. a vent for a gas stove would most definately not work and probably result in a fire. Metal flus for wood stoves would be "triple wall" with the inside section being stainless steel. This is specially made for wood heat and is pretty expensive. The other route would be the masonary flu with clay liners. Again expensive and would require major remodeling to put in.
If by chance your flu is the type designed for wood then I would suggest checking for an obstruction such as a bird nest in the flu.