Is the healing technique of Karate Kid practically possible?

The method is called Cupping therapy and is a form of alternative medicine.

A partial vacuum is created in cups placed on the skin either by means of heat or suction. According to the American Cancer Society, "[a]vailable scientific evidence does not support cupping as a cure for cancer or any other disease". It can leave temporary bruised painful marks on the skin and there is also a small risk of burns.

Being that it is an alternative medicine, some people will say it really works and some people will say it is "fiction".

By cupping with the help of fire or suction, a vacuum is created which creates localized inflammation proximal to the injured/diseased area. Inflammatory substances are drawn to the new area of inflammation by the body, the body rather 'prioritizes' the area to be managed by inflammation. This helps the sufferer to relieve of the suffering due to inflammation of the original site. Indian techniques of Ayurveda like 'agnikarma', now commonly done for conditions like plantar fasciitis also is thought to depend upon this ability of the body to 'camouflage' the original area of inflammation by creating a new area of inflammation nearby.

I believe it's something to do with acupuncture. There's two types indirect and direct In direct moxibustion a small amount of moxa is placed on top of an acupuncture point and burned. Direct moxibustion is a traditional technique considered to be very therapeutic. This type of moxibustion is further categorised into scarring and non-scarring. With non-scarring moxibustion, the moxa is placed on a point, ignited and allowed to remain onto the point until it burns out completely. This may lead to localised scarring, blisters and scarring after healing. The person will experience a pleasant heating sensation that penetrates deep into the skin but it isn’t likely they will experience any pain. The effectiveness of direct moxibustion particularly on immune function has been reported as early as 1927 by Dr Shimetaro Hara at the Kyushu University in Japan. Indirect moxibustion Indirect moxibustion is the popular form of care, there is a much lower risk of pain or burning. In indirect moxibustion a practitioner lights one end of a moxa stick, holding it close to the area being treated for several minutes until the area turns red. There are other forms of indirect moxibustion. For example another form of indirect moxibustion uses both acupuncture needles and moxa. A needle is inserted into a point and retained; the tip of the needle is then wrapped in moxa and ignited, generating heat to the point and the surrounding area. After the desired effect is achieved the moxa is extinguished and the needle removed.