Re: Identify unknown flintlock side by side gun
I am rather glad you had no caps, because firing a gun that might be loaded with an unknown powder and unknown projectile is never a good idea.
In fact, I strongly recommend not firing that gun at all. The barrels are almost certainly Damascus, made by wrapping white-hot lengths of iron and steel around a rod (mandrel) and welding them together with a hammer. Strong enough to pass proof when they were made, those barrels could well be dangerous today even with black powder.
13 is probably the gauge; in the muzzle loading days, shotguns could be ordered in gauges not available in our standardized era, where shotgun gauges go from 10 to 12 to 16 to 20 to 28. The gunmaker provided the appropriate size powder and shot measures as well as wads.
The gun was of moderate good quality when made, but not of high value. Double check to make sure there is no load in the barrels, then consider the gun a wall hanger.