I read an article, that said that the motor   'for the Vespa
was actually the  little gas motor that started
the ME-262 German Jet fighter  of WWII.

While modern jets have a power truck come up  along side
and start electrically, the ME-262 had a small gas powered motor to start the jet engines.

Okay,  it's wild to  even think   that on a jet fighter  to begin to crank it
you actually had  -a kick starter...  ?

                    

Hi lehaman and welcome to Posetteforever (and happy birthday too ) ...

What you wrote is a legend, but the "original" legend says that the Vespa engine was a kick start engine for the Piaggio fighter planes, but they had a sort of compressor to do that. It could neither be a kick starter for the ME 262 because that plane was german and even if you consider the alliances or sorts of WWII it's out of probabilities that Germans would have used an italian engine on a futuristic jet plane.... The link to planes is that the man who elaborate the concept was an aeronautical engineer who hated motorbicycles... You can read the whole story at wikipedia here

Under what circumstances?

"The idea was to design a cheap vehicle for the masses"