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In MN 55, the Buddha did not prohibit the eating of meat. This scripture concludes a monk cannot accept an offering of meat for food if it is known or suspected an animal was specifically killed for the explicit purpose of feeding a monk or monks.
Browsing the internet, my impression is leather is basically a by-product of the cattle & other animal meat & dairy industries. While animal rights organizations discuss the differences between leather as a 'by-product' vs a 'co-product', my impression is, in most cases, animals are not killed primarily for their skins. This situation appears similar to the principle the Buddha established in MN 55, where meat is not forbidden for monks when an animal is not killed specifically for monks.
In summary, while the Buddha exhorted laypeople to follow the Five Precepts, the 1st of which is undertaking the training to refrain from killing living beings; and while the scriptures also say carrying on a business of animals for slaughter is wrong livelihood for the business owner; the Buddha was silent about the finer details of how ordinary people should acquire food.
While I do not explicitly support the slaughter of animals, the problem with the arguments of animals rights activists is if there was no meat industry, the vast majority of cattle & similar animals would not even exist. The meat industry is a secular matter and not anything related to Buddhism.
In conclusion, it appears having a leather jacket would not be against Buddhist principles.