Expense is relative. I'd expect it to cost around $80-90. You need to find a vet that actually has experience with chinchillas if possible. Guinea pigs and rabbits at the very least. Cat and dog vets will usually not even see them. Initial visits are usually a little more expensive.
What they'll do is look at the feces under a microscope and try to make a diagnosis.
Can you tell me more about your chinchilla's diet? What kind of food is it getting, and what kind of pelleted diet, brand, type, etc? Treats that it has had and how much? That can be useful.
With digestive problems it's better to diagnose and treat as early as possible. Even a day or two can have a significant health impact. Also obtain syringe feeding supplies and a recovery diet such as critical care or lifeline. Monitor food intake carefully. Chinchillas are prone to GI-stasis where they stop eating and pooping. This can lead to fatal complications. If he stops eating you need to be prepared to hand feed. It's good to have supplies on hand regardless, especially since you have two chins. Weigh your chinchilla about once every three days to verify everything is okay and consult a vet. Normally they should be weighed about once a week so you know their healthy weight. Typically you will see noticeable weight increases the first four months after birth.
I did have a pet that presented with these symptoms once. It was diagnosed with coccidiosis. The count of coccidia spores was low and the vet wasn't sure it was significant but he responded to treatment after three days. The course of meds I think was ten days. After that I replaced all of the shelving and flooring in the cage to prevent reinfection. I have not had any issues since. But also my chinchilla had a very good diet, was not given treats, and was not stressed from relocation. Other types of parasites and problems can also cause soft stool. To be on the safe side I recommend getting a diagnosis by someone who knows what they are doing.