Howdy
The only way to know for sure is to proof it.
That means loading it, tying it down, and firing it remotely by pulling the trigger with a string or something.
If it does not blow up, it is safe.
You will get answers about Magna-Fluxing it, but that really does not answer the question, Magna-Fluxing will not find any tiny internal faults in the welds.
Damascus barrels consist of dozens of feet of twisted iron and steel bands, welded together. When they were new they would be proofed like any other firearm, by firing a proof load in them that was more powerful than a standard load. If the barrel did not blow up it was said to be 'in proof'. In fact, many Damascus barrels were stronger, when new, than some of the early fluid steel barrels.
But the problem is that over the years corrosion can cause voids in some of the welds. The voids can be internal, so there is no visible evidence of them, but they are still there.
I assume since you posted this question in the Black Powder section you would only fire it with Black Powder. I do know a guy who fires Smokeless loads in Damascus shotguns, but he is very experienced and knows what he is doing.
So really, the only way to know if the gun is not going to blow up on you is to tie it down and fire it remotely. Then you will know.