Explain an old gag?

Cafe Society
1

I was watching Martin and Lewis on the Colgate Hour through the miracle of DVD the other night. In one sketch, set at “Dean’s house”, Martin is talking to a network rep. Jerry comes through the yard flying his kite. The network rep asks if he could try it as he hasn’t played with a kite since childhood. Jerry gives him the string. The rep starts having fun with the kite. Jerry then says words to the effect of “c’mon mister I let you play with my kite …” (goes into his annoying nasal voice) “But don’t fly it!” Audience goes nuts.
The rep continues to play with the kite. Jerry then goes through a long list of things he wouldn’t care if the rep did with the kite and then concludes in the nasal voice with “But don’t fly it!” Audience goes nuts again.
Dean now starts on the rep about Jerry was nice enough to let the guy play with the kite and all the things the rep can do but (imitates the annoying Jerry voice) “But don’t fly it!” Audience pissing its collective pants it is laughing so hard.

Can somebody explain what all the hilarity was about? Was “But don’t fly it!” a catchphrase from the era with which I am unfamiliar? A punchline to a then-current joke? What?!

2

The only thing that occurs to me is that “flying it” is the only thing anyone would want to do with a kite. It’s like if someone asking whether they can use your car, and you tell them all the things they can do with it. But don’t drive it.

The audience was probably laughing more at the delivery than the joke itself. But I admit, it’s pretty lame.

3

The audience that night was made up entirely of French tourists.