You can let a chin chew cardboard, but not eat it. Ingesting cardboard can be bad for chinchillas. Also, I wouldn't let them have cardboard with ink on it. The ink could be safe, but why take the risk? I let my chins mess with some cardboard, but only during playtime when I can monitor the activity.
same here, Rhino only gets access to cardboard items when out for play time, and if i see him trying to eat any of it, i gently shoo him away from whatever box looks so tasty at the time.
I only allow cardboard at playtime for normal chins, malo chins I give them a cardboard box to strip, they just tear off strips and discard so they don't eat the cardboard but it gives them something to do to stave boredom.