It is absolutely not allowed to connect a wood stove to a chimney with other uses (no matter whether gas or oil) in addition.
If you no longer have an additional chimney, or want to install one, then the stove will no longer work. In this case, perhaps return or sell it. Which of course raises the question of why you did not clarify this before buying? That would be obvious before spending the money on it, wouldn’t it?
Furthermore, it depends on how many kW heating power the stove has and on the effective draft height up to the roof outlet. Only then can the optimal cross-section be specified or determined.