Seems like a dog kennel would be a nice size for four chinchillas as long as the bar spacing keeps them in and as long as the bottom of it can be kept clean. The problem is that if one has babies they could get out and die if the bar spacing is greater than 1/2" x 1". (I suspect that most dog kennels have 1" spacing or higher but it will depend on the design). Also the other problem is that males and females in the same cage will breed and that will be inevitable so you might advise that the breeding pair be kept in a smaller cage that is better set up for having kits.
If you want a chinchilla for yourself I would strongly recommend verifying that correct selective breeding practices have been followed and correct husbandry practices (Proper diet, access to chewing media, proper handling and room temperature guidelines, etc.) have been followed or you could face health issues and genetic defects down the road that may be pretty rotten to have to deal with. I speak from experience on this one.