He asked his father's friend, Charles C. Glover, president of the Riggs National Bank, for a job. Fleming started as a runner for Riggs on Pennsylvania Avenue in 1907. By 1925 he was running the bank - at age 35, the youngest bank president in the country.

By the early 1930s, American banks were in serious trouble. Fleming fought to protect Riggs and the banking system as a whole. He operated on three hours sleep a night, working with his general counsel to get Congress to give the comptroller of the currency the power to close DC banks in an emergency. At a time when many banks could be bought for next to nothing, Fleming did his best to help shore up shaky institutions.

President Franklin Roosevelt's inaugural message to "drive out the money changers" was not lost on Robert Fleming. He kept conservative bankers in check while winning the President's confidence in the ability of banks to adapt to new circumstances. Fleming was credited with shaping the legislaation that defined the American banking system as we know it.

His grateful colleagues elected him president of the American Bankers Association in 1935, the same year he became chairman of the board of Riggs.

Fleming headed Riggs for 37 years. He was also involved in the growth of the city his bank served. Fleming led the Board of Trade and chaired the board of George Washington University, where he had attended night classes in political economy and commercial law while working as a runner for Riggs. He looked after the finances of the National Geographic Society for years and was deeply involved with charities and institutions all over town.