You could always work with a nonprofit small animal rescue organization. Sometimes it isn't really worth it to go through and get your own nonprofit going. I've worked with nonprofit rescues quite a bit over the years, they have to do a lot of work to maintain the nonprofit status. Taking in rescues is something that you will find to be very taxing on you financially and emotionally. It isn't usually fluffy, happy chinchillas, it ends up being very sick and very neglected animals that require a lot of time investment and work. People bring you animals that they claim they love but the poor chins may be hanging on by a thread.
Don't get me wrong, helping the chins is a wonderful thing. It is extremely rewarding and the chins benefit from a loving person willing to care for them. However, unless you are in the financial position where you can pour hundreds or thousands of dollars into one chin (or possibly more or dozens) don't get into rescue. Also, if you don't have a lot of free time to devote to the chins, don't do it. Be prepared to keep every single chin that comes in because some chinchillas can end up being unadoptable for one reason or another.
So, basically what everyone has stated is very true! I take in a fair amount of rescues and all my money goes to their care...anything that I make selling supplies, in adoption fees and selling my own baby chins goes to rescue related costs!