Is the engine a Daytona 150F 4V, or 150FDX 4V Anima?
I wonder how the kick start shaft can slip out though?
There is a step on the kick start shaft inside the clutch cover, then there is a washer/shim that slip's over the shaft between the step and the clutch cover.
I can't see how it has happened?
See page 35/37 here-
http://mypitbike.ru/downloads/DaytonaAnima150.pdf
I hope you aren't paying too much for it, the engine need's to be taken out, head off, cylinder off, clutch cover off, clutch out, gear shift lever off, gear shift shaft out, and then the case's need to be split apart.
So you'll probably need a gasket set to go with the kick starter too.
It'll take you a couple of hour's to do the job, possibly longer if you haven't split an engine before.
Take lot's of picture's as you go for reference as you are reassembling it
Do you have any pictures of the bike ?
I reckon there might be something more to the problem?
Or it has chipped the kick start gear's and sometime's it slip's when kicking it over
That would need a new clutch basket possibly, or maybe a set of kick start gear's ?