I was really puzzled by this since kite-flying was a very basic feature of the Edo Period landscape. Kites fill the skies of Edo in ukiyo-e prints(1), boys run around with kites in art(2), literature, and memoirs, artists put out printed kites decorated with famous kabuki actors ( 3), and kite sellers walked the streets selling their coloured wares.
But, I also had a suspicion there might just be something to a kite ban. You see, the shogunate and the domains pretty much banned everything from time to time. Fireworks, silk clothes, colourful clothes, travel, dancing, music, the lottery, religious feasts, kabuki theatre, prostitutes outside the official quarters, the list goes on.
Sumptuary laws are laws that control how the population spends its money by trying to restrain "frivolous" expenditures and activities. They attempt to legislate frugality and "virtue" among the people, and in Tokugawa Japan, were often part of larger political and economic reform programs to reduce corruption, waste, and improve the economy, while giving aid to the needy. If people weren't wasting their money on frivolous extravagant things, and their time on useless pastimes, everyone would be better off. If every person acted according to their status in life - peasant, samurai, merchant - and didn't try to rise above that status, the world would be orderly and all would prosper. Or at least that's the Confucian ideal.
Just going by the number of Edicts issued against everything, you'd think Tokugawa Japan was a totalitarian state. The most strictly legislated class was the samurai, who were often forbidden to take part in all sorts of things that were not "appropriate" to their status: such as watching kabuki theatre. Then there were also laws to keep peasants and townsfolk from dressing above their station. But in reality, the rules were pretty bendable and inconsistent. Events like a recession could trigger big reforms with a flurry of new edicts, but these were the exception, and sumptuary laws would fade away until the next reform movement.
What does this have to do with kites? Well, I suspected that if kites had been banned, the most likely reason would be as part of a sumptuary law. I wasn't able to find any reputable reference to kites being banned in 1760 in English, and I did a quick google in Japanese, which didn't pick up anything obvious. (I don't read much Japanese, but enough to do a quick google check.) The reasoning usually given on the web and in trivia/craft books that report this story is that people were too interested in the hobby of flying kites and not paying enough attention to their work. This reasoning sounds exactly like an echo of a sumptuary edict, attempting to restore the proper order, so although I couldn't find a specific 1760 edict, I would not be surprised if there was one, it was mentioned in an English book I can't find, and it oddly became THE KITE BAN in English pop history.
However, I did find references to actual kite bans. The most detailed is in Gary Leupp's book Male Colors: The Construction of Homosexuality in Tokugawa Japan.
Similarly, a law of the second month of 1654 prohibited bannermen from a curious set of actions: flying kites, attiring manservants in beautiful clothes, and employing footboys as "objects of nanshoku."' These were no doubt seen as related phenomena: the lord pampered his beloved boy with gorgeous outfits and amused him with such pastimes as kite flying.
This sort of sumptuary law aimed at controlling Tokugawa retainers' behaviours and expenditures.
Much later, in the Tempo Reforms of the 1840s, fancy kites constantly made the list of extravagant toys that the shogunate demanded people stop selling and buying.
Despite the occasional edicts against extravagant kites and kite-flying, kites continued to be enjoyed by people, especially young boys who were expert kite fliers.