The photos don't demonstrate that KLOW aids healing. There was clearly no control group, and while it did heal nicely, the injury was largely a partial thickness or second degree burn, possibly with 2 smaller deeper spots (<1cm2) that would need to close from the edges — the remainder could heal from below. For that kind of burn on the hands, this rate of recovery isn't unusual; hands have a very good blood supply and typically mend fast. Another person brought up a foot burn that healed far more slowly, which makes sense: for hydrostatic reasons, foot wounds heal at roughly half the speed of hand wounds.
Whether KLOW has any effect, I can't say, but this doesn't prove it works. To me it looks like completely ordinary, average, expected healing for hands. Apart from the face, hands heal faster than anything else.