This is the second flag I know of that had "Seymour and Blair" on it - and the other one that I know of I have seen in a museum.
This had to do with the Democratic party candidates for the 1868 presidential election. Horatio Seymour was a former New York governor and his running mate was Francis Blair of Missouri (and former Union general under Sherman). His brother was Montgomery Blair, who was Lincoln's Postmaster general. Both Blair's were from St. Louis and were Republicans. Blair had also been a pre-war Missouri Congressman and had been in the Missouri state assembly as well.
They ran against U.S. Grant in 1868.
Hope this helps.