The problem with oats is they can be gassy, since chins can't easily pass gas it can turn into bloat which can be fatal. There are some that no longer even recommend them, or other grains as treats anymore do to the risk, and even when they were it was just a tiny pinch or about a few oats worth per week to avoid gas and that isn't enough to help with weight gain. Gas problems are pretty common, in a chin owners (mostly pet owners) FB group I'm in at least once a week someone is seems to dealing with a gas issue with their chins.
What are you going by to determine he is underweight? Just how much he weighs? or can you actually feel his bones? Is he healthy otherwise? and has he lost weight since the last visit or is it the same and just one vet says he is fine and the other says he is underweight? I know some vets think all chins are the same size and for example should all be 600-800g, but in reality they can very from about 400-1,200g or more and still be a healthy weight for their size.
If he is in fact underweight, as in when you pet him you can easily feel his ribs and spine, and you are feeding him all the pellets and hay he could want, then I would want to know why he is underweight. Chins should be able to maintain proper weight on good quality pellets and hay alone. If he is otherwise healthy and it's not a health issues causing it could he maybe getting too much exercise? Some chins need to have shorter playtime, like limited to just half an hour per day of out of the cage since they go go go the whole time they are out, similarly some can't have wheels since they over do it and burn too much calories. Also what kind of pellets are you feeding? and are you giving measured amounts or free feeding? Although I do measure mine to help keep an eye on his food intake and prevent too much waste if he tosses it, I don't restrict the pellets, just how much is in the bowl at any given time. If he finishes the two heaping tablespoons worth I give per day before the end of the day I do give him more. Some chins do need more food especially if they are very active, and it can vary from day to day so although most adult chins only eat about 2tb a day (even if free fed), some do eat a bit more and some a bit less, along with their hay.
If he really is underweight and there is no obvious causes, a better option then oats would be critical care. It's a recovery food for chins that are sick or recovering but is high in calories which will help him put on weight. You can also add a small amount of alfalfa to his diet, being a legume instead of grass it's higher in protein and fat which can help a chin gain weight, but it's also high in calcium so you don't want to give too much since some chins are prone to urinary tract stones. You can also try 3rd cut timothy hay, it's again higher in fat and protein which can help a chin gain weight, but not high in calcium like alfalfa so may be a safer option but normally needs to be ordered online, store bought hay is normally the 2nd cut which is standard feeding hay.
Hopefully they don't end up falling out. That is not normally even for a middle age chin (8-10 is only around 50ish in human years), if they fall out that will require regular teeth trimming for the rest of his life since the opposite teeth wont have anything to grind against anymore so they will overgrow. Also if any teeth are removed or fall out the remaining teeth can end up floating out of alignment as well since they aren't fixed into the jaw like human teeth.
