No, they cannot eat tree bark.
If they were able to, chinchilla would love to eat tree bark but it is not good for their health.
Therefore it is important to make sure your pet avoids eating tree bark.
It is too difficult for a chinchilla to digest tree bark. In addition they have very sensitive digestive tracts and tree bark may cause an issue.
So therefore do not feed tree bark to your chins as it is bad for their health.