Eliot Ness did a great deal of damage to Al Capone's operations, however he was not directly responsible for successfully convicting Capone of tax evasion.
Ness wouldn't have been going to the BOI, as he was not a BOI agent. Elliot Ness was a Special Agent with the Treasury Department. Since this was before the ATF, Bureau of Alcohol Tobacco Firearms and Explosives, existed investigating the illegal sales of tobacco and alcohol fell under the jurisdiction of the Treasury Department.
Ray refers to the Bureau as the FBI. However in 1927 it was called the BOI, Bureau of Investigation. The name wasn't changed to Federal Bureau of Investigation until 1935. But, Ray is from current time, so he would still refer to things with the name they have been known to Ray all his life. Ray may or may not be aware of the earlier name and name changing history, but it is not a class in history.
Elliott Ness didn't create the team to work with him until 1929, two years after this episode is set, although he did start working in Chicago in 1927.
Meigs Field (Merrill C. Meigs Field Airport) is shown on the map of Chicago, although the story is set in 1927 and Meigs Field wasn't built until 1948. It can't be a map from 2016, since Meigs Field was destroyed in 2003.
The Port of Chicago is located on the Far South Side, around 87th Street, not near Meigs Field as is shown on the map.