Which end of the shaft is stripped? If it is the outer end where the kick lever is attached, it could just be that the locking pin was loose, and the previous owner kept kicking it until the splines ground off (aka a moron). If it's the inner end, it could be that the motor was seized at one time and someone attempted to fix it with the kick starter. These are just speculations, but I would say that the inner splines being stripped would be the less common of the two occurrences.
To fix the outer end being stripped, tighten the locking screw on the kick lever as much as you can and then drill a hole through the side of the c-clamp on the lever, and into the shaft. Only drill a short distance into the shaft, enough for a metal pin to grab, when load is applied. Get a metal pin of the same diameter as the hole you drilled, and slip it into the hole. Cut the length of the pin in such a way to leave a slight gap between the outer surface of the c-clamp on the kick lever, and the end of the pin when the pin is pressed all the way into the hole. This allows you to place your weld inside that gap and sand it down so it doesn't look like you made any modifications.
The repair on the inner splines is a whole different ball game. I would consider replacing the shaft in that case.
Good luck!