i am so very sorry to hear this
i have no experience with kidney problems, however, i just want to tell you that they generally stop eating when there's something wrong, regardless of what it is. one of my chins has an allergy (to pollen, we're guessing) and she stops eating even when she's just having a flare up with that.
the important thing is to feed him, if you have to force feed him then that's what you have to do. this doesn't necessarily mean that it's extremely serious although it of course can be. oxbow critical care fine grind is great for syringing and he may even eat it off your finger (mae has done when she wouldn't have anything else but she had to be force fed on several occasions).
is he in pain? i'm guessing they are giving him pain relief? the thing with chins is that they don't show when there's something wrong and that's why they appear to go downhill very suddenly.
i'm not sure what to suggest vet wise. are there any other surgeries near you? i don't have an exotic specialist on the island but there are two vets at my surgery who are very good with chinchillas. perhaps you can ring the other surgeries - if there are some - and see if there's somebody who's experienced?
as for whether putting him to sleep would be the right thing to do.. you'll know. if you're force feeding and his weight doesn't even remotely stabilise, if he has absolutely no interest in anything and just lies there without moving, if he refuses to swallow food then it probably would be. get him a heat pad - mae for some reason finds it very comforting when she's sick. i've seen chins (well, mae) bounce back from what even the vets thought was the end.
good luck! xxx