How much vertical height can be added to the chin using fat graft?

Fat grafting is not a good way to augment the chin.
There are multiple reasons for this but the first one is that the chin does not have sufficient quality post tissue to support any significant graft volume. Whatever tissue is there is not good tissue to support grafted fat. fat that survives will be a small percentage and the remainder of the fat that will become necrotic will often be left in an unpredictable distribution. It is not an accepted standard procedure and with so many other excellent options you should pick one works, works well and is time proven.
The treatment options are sliding genioplasty, implant augmentation and the use of fillers. Those are all excellent treatments with a proven track record that work well.
It’s not a good area for fat transfer.
Fat transfer is inherently unpredictable, imprecise and unforgiving. Anytime you consider fat transfer you need to always ask yourself what is the plan if you don’t like the outcome?
If too much fat survives or the fat survives in areas where you don’t want it or it’s surviving one side but not the other what is the plan now?
Grafting tissues is not like injecting fillers using your own tissue. successful tissue grafting requires both quality tissue to be grafted, using excellent technique and finally having quality host tissue to support the graft. The chin does not have that. fat transfer is a better option for giving diffuse overall volume but is not good for giving very precise volume in small areas.
Fillers on the other hand are extremely precise, highly predictable and extremely forgiving.
If your gun shy about having surgery then fillers is the way to go. at least with fillers do you have a plan of action in case you didn’t like the outcome.
Best,
Mats Hagstrom MD