Generally speaking shotguns with Damacus barrels should not be fired at all, they are considered dangerous. Here is some information from the NRA website regarding Damacus barrel shotguns.
The best Damascus barrels made by Belgian and English gunmakers were regarded as strong and elastic. However, differentiating these barrels from the plethora of inferior-grade Damascus tubes produced all over Europe is a job for an expert. These barrels, made of soft iron poorly welded together, are not only weak, but also tend to rust and pit readily.
Some authorities consider the best Damascus barrels, properly proofed, to be capable of handling light smokeless powder loads. However, considerable expertise, probably beyond that of the average gunsmith, is required to determine which Damascus barrels are safe with such ammunition. With these considerations in mind, the owner of even a "best quality" shotgun with Damascus barrels should avoid firing the gun with any smokeless powder loads.