I believe it's supposed to be set in the early 1880s.
It was around that time that Mrs. Astor was forced to recognize the 'upstart' Vanderbilts, which the Russell family seems to mirror in the tv show. However, 'The Four Hundred' - the list of the 400 people who constituted 'Society', and based on the number that could fit in Caroline Astor's ballroom - was not compiled until the early 1890s, if I recall correctly. Since the list is already mentioned in the show, the program plays a bit fast and loose with the historical timelines.
Also, the marriage of Gladys to the Duke is also set 10 years earlier than it was real life, if Gladys is meant to be analogous with Consuelo Vanderbilt, who married the Duke of Marlborough in the mid 1890s.