I have a small chin. Could I increase the vertical height of my chin using fat transfer?

Dear Cherry Jagar,
Thank you for your question. Vertical length can be created using fat transfer, but the dimension of length becomes more challenging the greater the vertical increase due to graft survival. Silicone (not liquid, but solid implants) can create a more uniform shape that has definition, feels like your skeleton and is non-mobile. Hope this help you.
Be healthy and be well,
James M. Ridgway, MD, FACS

First and foremost I suggest you get a really quality assessment. Oral surgeons tend to do with this a little better than plastic surgeons because aesthetics of the lower 1/3 of the face are almost exclusively related to bone structure. This is especially true for young people.
Aging affects soft tissues more.
Realistic options for chin augmentation include fillers, implants and sliding genioplasty
Fat transfer is not a good option and will most likely leave you a disappointment.
Best,
Mats Hagstrom