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Hello. I'm sorry to hear about your dog.
With the known ingestion and now vomiting, I would start with x-rays. If there is an obstruction in the small intestine, which it sounds like, then he'll end up needing surgery to remove it. If it's just irritating as it moves through the intestine, then some fluids and multiple x-rays to follow the piece of leather as it is passed. I am worried that he'll end up needing surgery based on his history. X-rays will tell you for sure, though.
I hope this helps, let me know if you have any other questions.
If the vomiting stops and he is keeping down some pedialyte, then try some I/D or chicken/ rice. If he's eating and keeping it down, then an obstruction is unlikely. If the vomiting continues, then get x-rays.