We can read here:
In New York there were accounts of people feeling perfectly healthy when they boarded the subway in Coney Island and being taken off dead when they reached Columbus Circle.
The anecdote originates from The Coming Plague: Newly Emerging Diseases in a World Out of Balance by one Laurie Garrett (1994).
There were reports of women boarding a New York subway in Coney Island feeling little else than mild fatigue, and being found dead when the train pulled into Columbus Circle, some forty-five minutes later.
"There were reports" is a pretty safe phrase to use! In other words, this book is relating a rumor.
Garrett does not give a direct source for this. The next citation in the book is to Influenza: The Last Great Plague by W. Beveridge (1977), but Google Books is telling me that the anecdote is not in that source.
edit: I don't know why DavePhD deleted his answer, but he provided a similar anecdote from the New York Times Magazine in 1992:
One man got on a streetcar feeling well enough to go to work, rode six blocks and died.
This led me to another, from Lynette Iezzoni's Influenza 1918: the worst epidemic in American history (1998):
On a Cape Town trolley, the driver, conductor, and five passengers collapsed and died within a three-mile stretch of road.
This book is based on a 1998 episode of the PBS series American Experience.
None of these three secondary sources cited a primary source, but the core of the anecdote does seem a little more plausible now.