From a pet perspective this is what I would ask:
Personality of the chinchilla in question. Most hobby breeders should be willing to at the very least pull the chinchilla out of the cage, and see how it responds to being handled.
Ask about breeding: where did they get the breeders? Petstore? Rancher? Breeder?
Are they willing to answer your questions, and give you life long support for the chinchilla?
Do they "seem" reputable? Look around, the chin world is still fairly small and if theres something bad on someone it's sure to be out there somewhere.
If you can go to the breeders house(some don't allow customers in--thats fine), are the cages clean? Are the animals clean, cared for? Do they have fresh, drinkable water?