Sounds like Time and Again by Jack Finney. From Wikipedia's description (emphasis mine):
In November 1970, Simon Morley, an advertising sketch artist, is approached by U.S. Army Major Ruben Prien to participate in a secret government project. He is taken to a huge warehouse on the West Side of Manhattan, where he views what seem to be movie sets, with people acting on them. It seems this is a project to learn whether it is feasible to send people back into the past by what amounts to self-hypnosis—whether, by convincing oneself that one is in the past, not the present, one can make it so.
Si agrees to participate in the project, and requests permission to go back to New York City in 1882 [...] It is a huge fire, and Si and Julia find themselves trapped. They barely escape. Si learns that the building used to house the newspaper the New York World and one piece of the puzzle fits in—the missing word in Carmody's note was "Building". After watching the efforts to fight the fire, in which many die, the shaken couple returns to Gramercy Park. There is no sign of Pickering. [The burning of the New York World building is a factual historical event].
How I found it: when I searched Google for
time travel novel fire in New York, all of the top several results were about this book.