Premodern China had many unusual forms of torture, and an 1894 article about Tibet mentions that all its tortures are derived from China. Indeed, the "tradition" which you are asking about appears to be a description of lingchi 凌遲, which was developed in China. The 1894 article does not say that Tibetans practiced lingchi, and I have not heard of it from other sources.

According to the Tibetan scholar Gyelta Tsewang, in 1898 torture was abolished in Tibet; for comparison, the Qing abolished torture in 1905. Tsewang further claims that the prison Nangtseshar in which these tortures supposedly occurred never had room for more than 20 people, and the photos which are shared in some corners of the Internet of skulls and flayed skins are actually taken from other places. He points out that during the Cultural Revolution, innocent people such as Zhang Zhixin were raped and tortured by the Communists, so the conversion of Nangtseshar into an anti-Tibetan "torture museum" might seen as psychological projection.

My expertise is in East Asian Buddhism and I can say a little bit about accusations of using human body parts for "ornaments". There is very little evidence of body parts ever being used in rituals in Buddhist countries. The infamous medieval example of the Tachikawa-ryu Skull Ritual in Japan appears to be an outlier and it has been suggested that it is a work of creative writing which was never meant to actually be practiced. Tibet apparently had its own medieval example, a group of monks called Artso Bande Chopgye who performed ritual murders in the 11th century, inciting severe backlash. These rather gory and violent incidents are both medieval outliers which only drove the centralization and reform of Buddhism. There is not much different here from other parts of the world, e.g. one of the guys who ran with Joan of Arc also went on to a life of ritual abuse and murder. I think a "tradition" of human sacrifice surviving the medieval chaos would have been noted in Tibet both then and now; it beggars belief that no written record survives other than a "torture museum" created by the enemies of the Dalai Lama.

The claim being made of a "tradition" is highly dubious.