How far (in length) can you vertically lengthen a chin? (photos)

Vertical lengthening of the chin can be made with two different methods:
-the "step off" or bridged method: the chin is moved
forward and downward but the gap created is not filled by bone grafting,
but instead a rigid fixation plate holds the gap expeting for a
fibrotic fill up and eventually ossification; this methods allows no more than 5-6 mm vertical increase, and even though may fail to ossify the gap
-the bone supply
method (my choice and the way I do it regularly): harvesting a fragment
of elbow or chin bone to create the planned increase not depending on
the rigid plate gap; advantages are multiple: almost unlimited amount of
increase feasible, total versatility to perform complex or atypical
modifications, better long time stability, optimal ossification, no risk
of plate fracture, allows total creativity and not constrained by the
plate's limitations, allows more accurate calibration of the effect, etc; this method allows virtually unlimited amounts of vertical increase, it is all a matter of the right amount of interpositional bone graft applied, harvested from elbow or, should a large amount be necessary, from the iliac bone (hip).

Hi and thank you for your question.
I agree with Dr. Rodman that augmenting your chin with an implant (augmentation genioplasty) would not really add much in terms of vertical length of your chin, as it is specifically designed to increase chin projection (i.e. from side view) and horizontal width. A sliding genioplasty, where a portion of the bone is cut and mobilized/repositioned, can address vertical height in addition to projection so this could be an option, but surgery is somewhat more involved with longer recovery. Mentoplasty, the process of actually reshaping/contouring the jaw bone underlying the chin, may also be an option to achieve a more "chiseled" look. 
A consultation with a specialist in facial plastic surgery to assess your individual needs is crucial to be fully informed of your options. Hope that helped.

Thank you for sharing your pictures and your question.  
First, you are lovely, with great lips, full cheeks and nice face shape.  You certainly don't need much!
If you are interested in a chin like the one you posted, I would recommend an osseous genioplasty.  Genioplasty is the only way to increase vertical length significantly (implants give projection horizontally but not as much vertically).  One can get quite a bit of vertical distance with a genioplasty, but needs a signficant jump bone grafting is required.  That would not be the case for you.  For you I would recommend a vertical lengthening and horizontal narrowing genioplasty.  This would mean moving the chin bone down a bit and shaving down the sides to make it more narrow.  It is definitely doable!
Best of luck
Dr Rodman

Altering the height and shape of the chin is common. The key is to blend the jawline properly so the definition and contour is 'even'. Often the 'bite' is less ideal even when orthodontics has been done; but masking  the appearance with a genioplasty is indeed feasible