A synonym of Indian burn, the term Chinese burn, also chinese burn, originated in children’s slang to designate a juvenile torment inflicted by grasping a person’s wrist or forearm with both hands and twisting the skin sharply in opposite directions, causing a painful burning sensation. This term occasionally occurs in extended use.

The allusion is to the fiendish methods of torture attributed to the Chinese.

These are the earliest occurrences of the term that I have found, in chronological order:

1-: From Whizz for Atomms: A guide to survival in the 20th century for felow pupils, their doting maters, pompous paters and any others who are interested (London: Max Parrish and Co. Ltd, 1956), by the English author and journalist Geoffrey Willans (1911-1958) and the English artist, cartoonist and illustrator Ronald Searle (1920-2011):

DET. INSPECTR THE HON NIGEL MOLESWORTH: Now you kno the rule in cases like this the smallest tick hav to own up. What an exquisite vase Lord Weevil. Is it ming?
A VOICE: Wot hav that got to do with it?
DET. INSPECTR THE HON NIGEL MOLESWORTH: Detectives are very cultured. Come on grab him by the neck scrag him give him a chinese burn beat him up and let him hav it. Tung Fifth dynasty? You surprise me. i would not hav thort that tint of eggshell blue – no matter, tie his hands behind the chair. Now, scum, are you going to own up?
No, o no i am inocent.

Come on grab him by the neck scrag him give him a chinese burn beat him up. Tung Fifth dynasty? You surprise me

2-: From The Lore and Language of Schoolchildren (Oxford University Press, 1959), by the English folklorists Iona Opie (1923-2017) and Peter Opie (1918-1982):

Unpopular Children: Jeers and Torments
TORTURES

The most common torture is to ‘do a barley-sugar’, also expressed verbally in the threat ‘I’ll barley-sugar you’, which is to twist a person’s arm round until it hurts, usually behind his back, so that the sufferer has—according to which way his arm is being twisted—to lean backwards or bend forwards excessively to alleviate the pain, and is thus utterly at his tormentor’s mercy. The hold is also known as ‘Red hot poker’, ‘Fireman’s torture’, and ‘Nelson’s grip’ or ‘Nelson’s twist’ (after the wrestling hold).
Less dangerous, but equally painful, is a ‘Chinese burn’, also known as ‘Chinese torture’ and ‘Chinese twist’ (in the United States ‘Indian burn’ or ‘Indian torture’), in which the perpetrator clenches the victim’s wrist with both hands and ‘twists both ways at the same time, like wringing the dish cloth’. This torture is particularly unpleasant if the victim’s arm is already twisted behind his back. If the operation is conducted merely by squeezing a piece of flesh between the thumb nails and rubbing in opposite directions it is termed ‘Snake’s bite’.

The term barley-sugar occurs in the comic novel Vice Versâ: or, A lesson to Fathers (London: Smith, Elder, & Co., 1882), by F. Anstey, pseudonym of the English author Thomas Anstey Guthrie (1856-1934)—through the use of a talisman, Dick Bultitude, a schoolboy, has swapped bodies his father, Paul Bultitude, a pompous businessman; this results in the father suffering at ‘Crichton House’ boarding school while Dick is able to enjoy his father’s much more comfortable life:

‘Will you promise on your sacred word of honour, now, to be a decent sort of chap again, as you were last term?’
But Mr. Bultitude, though he longed for peace and quietness, dreaded doing or saying anything to favour the impression that he was the schoolboy he unluckily appeared to be, and he had not skill and tact enough to dissemble and assume a familiar genial tone of equality with these rough boys.
‘You don’t understand,’ he protested feebly. ‘If I could only tell you—’
‘We don’t want any fine language, you know,’ said the relentless Coggs. ‘Yes or no. Will you promise to be your old self again?’
‘I only wish I could,’ said poor Mr. Bultitude—but I can’t!’
‘Very well, then,’ said Coggs firmly, ‘we must try the torture. Coker, will you screw the back of his hand, while I show him how they make barley-sugar?’
And he gave Paul an interesting illustration of the latter branch of industry by twisting his right arm round and round till he nearly wrenched it out of the socket, while Coker seized his left hand and pounded it vigorously with the first joint of his forefinger, causing the unfortunate Paul to yell for mercy.

3-: From The Rachel Papers (London: Jonathan Cape, 1973), by the English novelist Martin Amis (born 1949):

For goodness’ sake, I had had only one real infection. The rest was temporary scares and growing neurosis about my private parts—parts (it bore pointing out) that had come to enjoy greater privacy over recent months. Now I looked at them only when I had to, and even then covertly, as if I were a queen and they were someone else’s. Any spot or abrasion, even when I knew perfectly well it was a zip-scar or the remains of some tortured blackhead, meant going through the routine. It meant working it over. It meant waiting for the one-by-one elimination of my senses. It meant another trip to the local library, another afternoon browsing pinkly through medical dictionaries, ship’s doctor’s manuals.
Let is just try anything when I had a pee and Christ would I show it who was boss. I washed, got out, slipped a towel over my shoulder—had a pee. I couldn’t tell whether it hurt or not. So I worked it over anyway, and good.
Normal procedure: I flicked it; slapped it; I garrotted it with both hands; a final searing chinese-burn—a last attempt to tempt out a drop of that most dreaded commodity, discharge.

4-: From The Guardian (Manchester, Lancashire, England) of Wednesday 4^th July 1973:

The mother of a 3-year-old boy told Leeds Crown Court yesterday that the man she lived with balanced on one foot on the child’s stomach. The child, Darren Robinson, was also beaten with a belt, force-fed, and locked in a dark cellar, it is claimed.
Susan Robinson (25), who has admitted four charges of cruelty and assault against two of her children, claimed that Michael Brady, the man she lived with, also gave the “Chinese burn” to her youngest child, Gary, aged 7 months.

5-: From The Secret Kingdom, an investigation by June Johns into the world of children, published in the Liverpool Echo (Liverpool, Merseyside, England) of Tuesday 10^th September 1974:

One of the reasons children are eager to obey the stringent rules of street games without demur is their need to be like everyone else. To attract attention to oneself is to invite ridicule or even rejection, and children have no inhibitions in telling a misfit that he’s not wanted. Sometimes he becomes acceptable if he suffers “torture” without crying or telling tales.
‘Chinese burn’ is the most popular—to the torturers at least. More dangerous is ‘red hot poker’ or ‘Nelson’s twist’ in which the arm is twisted behind the back.

6-: From a book review, published in The Guardian (Manchester, Greater Manchester, England) of Thursday 5^th June 1975:

Skirmish, by Clive Egleton (Hodder, £2.95).—Fast, brisk clipped-voice thriller: follows attempts by inept Moscow-directed heavies to assassinate British Intelligence Major: grips like a Chinese burn and, despite a call girl in suede underwear, is just as boyish.