The Wuhan virus is one of numerous kinds of coronaviruses, including those that make up the common cold. I don't think it's possible to stop viruses like this from actually spreading so I suspect most people will eventually end up with it like the other kinds of coronaviruses that afflict humanity each year.
The COVID-19 epidemic has been politicized beyond belief as if government can somehow determine the success or failure of containing something that I very much doubt is containable any more than the seasonal flu. Flu has proven to be much more deadly this year. As more statistical data is gathered on those who have the virus who are not hospitalized with it, I think it becomes apparent it the symptoms and mortality rates are more in line with severe seasonal flu than the end-of-the-world like the media is hyping it up to be.
Those hospitalized with the flu have similar experiences to those hospitalized with COVID-19. (The 19th documented coronavirus)
In order for a virus to infect cells, its protein structure (proteins are assembled based on genes) must be chemically compatible with protein structure the cell wall of the host in order to penetrate the cell and infect it. Since humans and animals are not genetically similar it is unlikely that are both hosts are compatible with the same virus. Sometimes there are overlaps though.
Much more is known about SARS, another novel coronavirus that was documented in 2014, is similar in many ways to the Wuhan coronavirus and has been studied for years. Comparisons were made with proteins responsible for penetrating the hosts's cells between SARS and COVID-19. It turns out swine, cats, ferrets, and primates could be susceptible to infection. I think there is good evidence that cats can catch SARS and develop symptoms.
Rodents are not a good match, are considered to be resistant, and therefore are not being used for laboratory models in the study of COVID-19. So to answer your question, it appears that chinchillas cannot become infected with COVID-19.
There has been some concern about dogs. There was a PCR test done on a dog in Hong Kong where the virus showed up on the test as a weak match. Its owner tested positive for the virus which is why the dog was tested. It is still possible the dog's test was botched with contamination of virus particles from the owner. PCR tests use samples taken from the inside of the nose. Consider that the test showed only a weak match, the owner was in regular close contact with the dog, and the dog never showed any symptoms. I am skeptical the dog actually caught the virus. Nothing was said if there were antibodies found but I think that would be much more conclusive.
Even if animals do get the virus they won't necessarily be able to transmit it to humans as even more factors must be present for actual communication of a virus.
You can read more on this here:
https://www.wormsandgermsblog.com/2020/02/articles/animals/cats/covid-2-and-potential-animal-hosts/and here:
https://www.newscientist.com/article/dn4329-cats-can-catch-sars-and-pass-it-on/
