Looking at my Terminal Area chart, there is no "flyway" identified as
such.

However, if you are under 1900' MSL and stay just north of the
Freeway, I'd say you wouldn't have to talk to anybody. You could
check with Midway ATIS to see what freq they are guarding for radar
contact and let them know what you are doing.

This isn't a route for the faint of heart - as someone else has
observed, there is no place to land except the occasional railroad and
at 1900 ft you don't have much choice anyway. Even Meigs has been
covered with trees and shrubs.