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.
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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.