Here is the occasionally NSFW text of the letter he sent (source):
Dear Mrs. Budd. In 1894 a friend of mine shipped as a deck hand on the Steamer Tacoma, Capt. John Davis. They sailed from San Francisco for Hong Kong, China. On arriving there he and two others went ashore and got drunk. When they returned the boat was gone. At that time there was famine in China. Meat of any kind was from $1–3 per pound. So great was the suffering among the very poor that all children under 12 were sold for food in order to keep others from starving. A boy or girl under 14 was not safe in the street. You could go in any shop and ask for steak—chops—or stew meat. Part of the naked body of a boy or girl would be brought out and just what you wanted cut from it. A boy or girl's behind which is the sweetest part of the body and sold as veal cutlet brought the highest price. John staid there so long he acquired a taste for human flesh. On his return to N.Y. he stole two boys, one 7 and one 11. Took them to his home stripped them naked tied them in a closet. Then burned everything they had on. Several times every day and night he spanked them – tortured them – to make their meat good and tender. First he killed the 11 year old boy, because he had the fattest ass and of course the most meat on it. Every part of his body was cooked and eaten except the head—bones and guts. He was roasted in the oven (all of his ass), boiled, broiled, fried and stewed. The little boy was next, went the same way. At that time, I was living at 409 E 100 St. near—right side. He told me so often how good human flesh was I made up my mind to taste it. On Sunday June the 3, 1928 I called on you at 406 W 15 St. Brought you pot cheese—strawberries. We had lunch. Grace sat in my lap and kissed me. I made up my mind to eat her. On the pretense of taking her to a party. You said yes she could go. I took her to an empty house in Westchester I had already picked out. When we got there, I told her to remain outside. She picked wildflowers. I went upstairs and stripped all my clothes off. I knew if I did not I would get her blood on them. When all was ready I went to the window and called her. Then I hid in a closet until she was in the room. When she saw me all naked she began to cry and tried to run down the stairs. I grabbed her and she said she would tell her mamma. First I stripped her naked. How she did kick – bite and scratch. I choked her to death, then cut her in small pieces so I could take my meat to my rooms. Cook and eat it. How sweet and tender her little ass was roasted in the oven. It took me 9 days to eat her entire body. I did not fuck her tho I could of had I wished. She died a virgin.
I don't see a specific textual echo, but compare to the memoirs of George Psalmanazar, the famous fraudster.
http://en.wikipedia.org/wiki/George_Psalmanazar
Psalmanazar was an early eighteenth-century personality who showed up in England claiming to be a self-exiled prince of Formosa (aka Taiwan). He enjoyed celebrity for some time with his book - a fictitious travelogue -and his excellence at conversation. He would tell tall tales, speak "Formosan" at parties, &c. It's all pretty fun and madcap.
The key part though is that he describes a similar mass-slaughter and cannibalism of children in Formosa, albeit ritualistically in this case:
Annually they sacrificed the hearts of 18,000 young boys to gods and priests ate the bodies.
Psalmanazar's book was really popular. Swift cites him as an authority on the feasibility of cannibalism in A Modest Proposal (a joke on Swift's part, as Psalmanazar had many skeptics, and had been exposed as a lovable fraudster by the time that Swift wrote).
How popular was it by the late nineteenth century? I have no idea, but the legend of China as a meat market for children's flesh had been long in play, and might have, if indirectly, informed this crazy person's ideas. Even the "eat children as a response to starvation" aspect just sounds like Swift to me, and I know people were still reading Swift in the late nineteenth century (Gulliver's Travels has never been out of print).
I'm not familiar with any cases of cannibalism in either Hong Kong or during this time period. However I did write a research paper on supposed cases in southern China during the Great Leap Forward and the resulting famine.
There's a book I used for my paper that recounts purported cases throughout that period of Chinese history. I forget the book's name and scholar's name but it mainly focused around some grim cases in Guizhou.
Recently I finished the book The Corpse Walker which is a series of oral interviews by a well known Chinese writer Liao Yiwu. Within the book he interviews two different people who attest to witnessing examples of cannibalism during the Great Famine. I bring this up because one man in particular goes into great detail about he and his patrol unit breaking up a cooking party in which a family was cooking their daughter for food.
Last, and more related to your time frame than the above, is that some scholars have argued that the subject theme of Lu Xun's Diary of a Madman hints that cannibalism, while taboo, may have been somewhat common knowledge. Whether it was true or just a feared subject is a different matter.
Related to the OP's question - could this have had a basis in anti-Chinese literature/propaganda from the time?
A good place to start might be Mike Davis's Late Victorian Holocausts. On page 76 he writes of the 1878 famine, "[Missionary Timothy] Richards later discovered human meat being sold openly in the streets and heard stories of "parents exchanging young children because they could not kill and eat their own." He quotes the journalist Francis Nichols as saying the following about the famine of 1901: "By-and-by human flesh began to be sold in the suburbs of Sian. At first the traffic was carried out clandestinely, but after a time a horrible kind of meat ball, made from the bodies of human being who had died of hunger, became a staple article of food, that was sold for the equivalent of about four American cents a pound." p.178
I could probably find more, but it has a piss-poor index without a mention of cannibalism!