I would have to say in my opinion, which I have had this happen with females, and males, who have had cagemates their whole life, and due to a death or other circumstance, needed a new cagemates, this has happened. To be honest with you, I tried the bathroom thing, holding them at the same time, the cages next to each other ( all they did was pee on each other) and in my OWN experience, this is what has always worked, and it has never failed me:
You know those 1,2,3, plus metal carriers us chin people seem to have in abundance? If not, you can usually buy them for 10 a hole from a breeder who may have extra, it has always started with those. The holes are smaller, and although they always fit one chin comfortably, when you put two in there, they do NOT have much room to go at each other, and they are both very aware of that. There are two different ways to doing this, and yes, it is the "smoosh" method said by Diva_Chins. Although the poster below said it does not establish dominance, well no, not immediatly, they will do that when they later get in the cage, at least in my experience. The reason I keep saying in my experience, is because I know that not one answer is right, and I dont want you thinking one way over the other is better or the only way. This is just what always works for me.
On mild cases , I have put the two I want to get along in the same hole. I leave them for at least 4 hours. I have an outside water bottle I can hook to it, and a bowl that I can bolt on with some pellets, not because they are going to die in 4 hours without it, but because, as I have seen in my experience, some of them, after being in there for an hour or so, have eaten with the others, and that is a sure sign things are going good. I always cover the bottom with fresh kiln dried pine,, which is the bedding I use, and put a stick or two in there, which they usually share too at the end. Almost all of the time, by the time is up, they are laying on top of each other, and no kaking is heard, and they are being polite when they need to move, Occasionaly when I take them out to put them into a new, clean cage neither has been dominant in before, they will be wet on the back or other area, meaning they have initially peed on each other. I offer them baths, and most of the time they try to jump in together. Mind, this is with females, or male, female pairs.
For the ones that seem to be ok, and then all of a sudden one turns to face the other, and I hear kaking, although I have never had fur pulling in the smoosh method, I pick up the carrier after starting the truck if it is winter, put a blanket over it for the carry to the car, so no deafts effect them, and then I take the blanket off, put on the music, and we go for a nice long ride. I dont know why, but I have heard multiple times that chinchillas often bond best during times of stress or uncertainity, and this has never failed, with males, females, or male female pairs. In the case of male female pairs that I want to breed and introduce because they did not initially get along in the males cage, and then a neutral one, the male almost ALWAYS develops dominance, although dont get me wrong, it is not like thinking people male female dominance.
For my small herd ( about 15) the male usually always knows when to back off, without having to have his fur pulled out or being sprayed. I notice he only tried to mate usually when she is receptive, and he treates the females he is in with well, he cuddles up with them, grooms them , etc, no problems.
For the males that accept male partners, I think there is one big rule : They should really be young, less than a year, and as young as you can get them to put them together. I have an example, I have two males, they have been together since weaning, too early at my opinion, but the breeder weaned them at 6 weeks and put thm together. They are completely different colors, and grew up together. They can be seperated for months mating in different cages, and always returned welcoming each other. However, when I try to take one of them seperate, and have him be a cagemate to another male, smoosh method or not, the one that has been bonded since babyhood, reacts very violently.
I currently have a male, who had a sapphire male cagemate. The sapphire, believe it or not, was a rescue. So was his outstanding cagemate. Although both came with extensive pedigrees, they ended up with a person who couldnt take proper care. I gave the sapphire to a friend who is concentrating on sapphires, because I believe in order to help that mutation AT ALL, one needs to concentrate very specifically on that only color. Which I am not able, or wantng to do.
So, I need a male cagemate for his buddy who I kept, who fts with my other chins. He is considered a real "chocolate" or dark tan, with ebony in his lines, beige, pink white, etc. He is a huge, sweet boy, and he has no discrimination against any male chinchillas, despite him being five. I am thinking I need to put a young male in with him.
Anyways, I hope this gives you some insight into how some of us introduce. It is easier the younger they are, and it is easier if you put them in a situation that may seem stressful, like a car ride , but NOTHING that will endanger them. Good Luck.