I think with the dogs it varies from one to another.
My sister has a yellow lab (about 90 lbs) and the dog thinks the chinchillas are her babies. whenever they cry she runs to the cages and checks on them and she has saved about 4 lives by finding them when our dad left the cage open and they have gotten out. they have to be really careful though because as much as she loves the chinchillas she is a little clumsy.
My husband's dog on the other hand...it thought the chinchillas were food. he ended up having to find a new home for the dog because it was causing my chinchillas too much stress. it was a small dog, a shiba inu.
make sure the chinchilla is safe with whatever animals you introdue it to. and something to keep in mind, if the chinchilla feels threatened by the dog, it may spray, i've had to clean my couch a few times after the cats started to annoy the chinchillas.