Hi!
So I just wanted to chime in a bit about milk replacers, because it is a topic very near and dear to my heart... I am a wildlife rehabilitator and nutritionist, and part of my job is spent entirely on formulating milk replacers for various mammalian species we care for at my center. Chinchillas are not one of those animals, but I can provide the basics of the theory for your info. This is just the tip of the iceberg, but I hope it helps...
So, the basics:
Wild mammals all produce milk, but not all milk is the same. The milk for a human baby is different than the milk needed for a calf to develop; in the same way, your chinchilla's needs will be different than the needs of a kitten, puppy, rat, rabbit, or guinea pig. All baby mammals need fat and protein, and no fiber in their milk. They also have different levels of total solids, or the percentage of the milk that isn't water. Some animals have very dilute milk (opossums, for example) while others are so concentrated the milk is thicker than cottage cheese (many fur seals). Although there are many differences between individual milks on a chemical level, there is not enough information on any species' milk (except cow's) for us to know exactly how they differ. So we use the limited information that we have to do the best we can; usually with the "macronutrients" or fat, protein, and total solids.
All brands of commercial milk replacers (esbilac, KMR, LMR, multimilk, etc) are made of the same basic ingredients - usually various parts of whole cow's milk, dried, separated, dehydrated, and recombined to create different balances of nutrients appropriate for baby animals to grow (which animal depends on what they are designing the diet for). There are some based on goat's milk, but the truth is that none of these milk replacers are significantly different from one another in terms of the base ingredients (milk fat is essentially milk fat for all species). Where they DO differ is in their protein and fat balances.
This is where many people go wrong. If you give a baby mammal the wrong balance of protein and fat, they will not thrive. They will either loose weight, or develop gastrointestinal issues like diarrhea or gut stasis. As we all know, these problems can be life threatening and difficult to reverse. The problem is knowing exactly what is required!
Keep in mind that like all pet products, commercial milk replacers are not regulated closely enough to be very reliable. Very little information is required by law to be provided with pet products. Unlike human grade products, they are only required to list 5 things on their labels: Minimum protein, Minimum fat, Maximum fiber, Maximum moisture, and the ingredients in descending order of proportion. There are many loopholes in these laws that allow products to be highly variable - but that's a discussion for another time! The point is, you really only know the company's claim as to the minimum protein and fat; it all depends on if you trust the company or not. Some companies are more reliable than others; for example, mother's helper is awful while KMR (petAg) is reasonably trusted to be what it says it is. However, recently there have been some quality problems with petag as well, so all I'm saying is there is no guarantee.
Having said that, we all do the best we can, and everyone will have a different opinion on what you should do and what works for them. Home recipes using human grade foods have more basic nutrition information available and the ingredients have more reliable quality. The problem with various mixes or home recipes is that you need to crunch some numbers and figure out what your overall basic nutritional analysis will be after the ingredients are mixed, and most people do not know how to do that... so it is hard to narrow the field. The ingredients might be good in the right proportions, but maybe the success with that formula is incredibly low because the balance was off - in other words, you probably could make a goats milk/heavy cream mix that was perfect for chinchillas - but 1 part goats milk to 3 parts heavy cream is very different from 2 parts goats milk to 2 parts heavy cream. In order to get the right balance, you have know what fat/protein ratio you are aiming for AND do the math to figure out how to mix the ingredients. Most people, vets or not, don't know how to do that. Plus, as far as I've seen (someone correct me if they know) there hasn't been a study done on the specific milk composition of chinchillas - so how do you estimate your target?
We have to make educated guesses. There are some "clues" like the correlation between growth rate and total solids (ie. faster means higher). Also, species with similar growth patterns will be similar - but realize this doesn't mean closely related species! Hares and cottontail rabbits are pretty closely related; they look similar and they eat the same things when they are grown up. However their milk needs are wildly different - because hares are precocial (like chinchillas, they are born eyes open and more independant) and cottontails are altricial (born hairless and eyes closed). Figuring out what an animal needs takes research, trial and analysis, and more research. Since I don't work with chinchilla babies, I haven't done any of the research. From my experience though, it would be reasonable to say that an adequate formula could be extrapolated from hare formula, just based on similarities in development - and I'm not at work, but if you want I can give you those values tomorrow. I can also give you a cleaned-up and simplified version of an excel recipe calcuator, if you want to play with it and see what the different recipes end up looking like.
I would tend to trust long time breeders over vets. Realize though that there is a certain mortality level that is accepted when you have a certain number of animals to care for - so although a formula "works," it may not actually be ideal - in fact, survival may be quite low (animals are amazing, even with the worst formula possible, some will survive). I doubt that most breeders have actually run statistics to figure out how many of their hand-fed babies make it - or that smaller breeders have a large enough sample size to really say it was the formula and not chance or another factor.
Anyway, there's a crash course in milk composition macro-nutrition. It isn't everything there is to know, and it probably won't help you feed your little baby chinchilla if something were to happen. But I hope it gives you some of the knowledge you are looking for! I always feel better when I understand something thoroughly
Sorry for the long post!