How long have they had their new cage? Are there new shelves in it?
I think you'll find they'll get quieter as they get used to their cage. Also chinchillas love to break the corners off of new shelves which could be happening.
If your cage has plastic parts and plastic shelves and they are chewing on plastic they need to be moved into an all-metal cage. Chinchillas love to chew plastic, escape from cages that have plastic floors, and can die of complications from eating plastic.
Of course chinchillas are active mostly after sundown and that is a good time to turn the lights on and observe them and see exactly what they are doing. I suspect they are exploring the new limits of their cage. There is also some novelty of chewing on bars for some reason. Mine have removed the powder coat in a couple of spots.
Also if you have an exercise wheel or two that can help. I have one for each of my two and it has cut down on a lot of noise. Make sure the shelving is secure. Adding a couple more shelves and securing them well to the bars can help with bar rattle depending on the cage. Also I wear ear plugs at night because no sound proofing, toys, wheels, etc. in the world will stop chinchillas from making nighttime noise. My Spot will even squeal and scream at weird hours just for the heck of it.
