Real Life People?

There was a Dr. Vose in Fall River, but he wasn't a Psychiatrist. He was a medical doctor who performed back alley abortions. He actually killed a woman in this process (accidentally), and hid her in a trunk in his attic. He was finally caught and went to prison, but not for the rest of his life.

There was also really a William Borden who was widely believed to be that bastard son of Lizzie and Emma's Father, Andrew. He was mostly disowned by the family, and did die by hanging. But, unlike in the series, he was not murdered by Lizzie. He fell on hard times and hanged himself in the apple orchard behind his house. So his death by hanging in the show was based on fact.

The Trotwoods are pure fiction. The name of the family was taken from a character in Charles Dickens' novel David Copperfield.

Mr. Flowers is also a purely fictional character, but there was a very real Red Light district in Fall River known as Jerusalem Row. Characters like him did exist, but so far as anyone knows for certain, none of them went by that moniker.