I am so sorry for your loss.
Delivery is pretty quick for chinchillas. In my herd I don't notice much of a change the day before delivery, other than some girls will drain their water bottle just before. Once labor starts you may notice stretching, panting, and an overall uncomfortable chinchilla. The delivery is ppretty fast.
Since your chinchilla seemed to labor for over 24 hours and the baby was hanging out for such a long time there was obviously a serious problem. I'm really surprised that the baby was born alive at all. My point is that there is no way to know what happened internally. That was a lot of stress for her to handle (bad labor, vet visit, death of baby, ect) Chinchillas have died from shock due to stress. So, most likely it was a direct result of the problem delivery and not the vet that took the life of your chinchilla. Unfortunately, you will probably never know for sure.