The U.S. double gun makers began introducing fluid steel barrels in the mid-1890s. Parker Titanic steel barrels were offered for Grades 3 - 6 in 1897. It is my opinion that by 1900 most new doubles were supplied with fluid steel.
Some however were not enamored of that new fangled stuff
The latest Parker hammerless damascus barrels recorded are SN 221,278 12g GH D3 1927, SN 222,845 12g DHE D4 1927, and SN 227,020 12g VHE D3 1928.