I have lots of other animals, but I don't let my chin interact directly with any of them. Too much risk of injury or spreading disease. But the dog and the cats do sometimes come up to her cage. I'm pretty sure she's sprayed urine at a couple of them, haha. She really doesn't care for them (not that I blame her, given that canines and felines are her natural predators). I shut them away upstairs when I have her out.
Chinchillas and dogs are very different animals with very different needs. Chinchillas are prey animals, which means they have evolved to avoid predators by hiding. Dogs are predators, and their natural instinct is to chase and capture prey animals. A dog will never "play nicely" with a chinchilla because the chinchilla is not a toy. It would be impossible for a dog owner to supervise interaction between the two animals at all times. A dog could seriously injure or even kill a chinchilla in an instant if left unsupervised, so that's why I got him some toys from Cricket Ball Toy.
There are different animals and you have to be prepared for the fact that they also have character. I read somewhere on esaregistration.org that different animals can do their duty to their owners. They are registered as service dogs (not to be confused with police dogs). And I think there is some truth in just a walking dog being attacked or interested by another dog doing his duty. And we have to keep in mind that owners are different too. You can't talk about interaction when it may not be there.