I know that Hawthorne leaves are used by some people with chins who have heart conditions, but I couldn't tell you on the berries. Personally I'm a little weary of anything I don't see mentioned on CnH as totally safe on a regular basis.
I saved a list of safe herbs I found a while ago, and Hawthorne leaves are listed as safe, but nothing about the berries. Bovril is right, it's for heart conditions. Can't be much more help past that though
It has a lot of benefits but it is also a blood thinner/anti-coagulant. If your chinchilla gets cut it will bleed a LOT. This is why they are so good for cardiovascular issues, but taken in high doses they really thin the blood, hence the dizziness side effect warnings.
Remember chinchillas weigh ~1 pound. In relation to how much an average human would consume they are getting 150 times the dose. )
Edited to say: There may not be an issue with feeding them to chinchillas but this is one of the herbs I won't give to them because I've taken it myself.
I've been giving my boys Tanya's supplement, which contains a few of the Hawthorne berries in a 1 lb. bag, at least 2-3 times per week for over 3 years and have had absolutely no issues. But as I've mentioned all treats should be given in moderation & very small amounts.