Is it possible to know for sure who invented the kite? No it isn't, but most research points to the Asian region - many hundreds of years BC!
While researching other history pages on this site, I got the impression that China was the birth-place of the kite. However, on re-searching the Web, it seems that the kite idea might have been independently discovered in Malaysia as well.
From these 2 regions, kites spread first to the rest of Asia, then eventually to the rest of the world.
Interestingly, a few specific names do turn up in ancient Chinese literature. Here's a few, each of whom might have felt that they were the one who invented the kite in China...
In addition to these facts gleaned from actual written records, there is also a traditional belief or legend regarding who invented the kite. The story goes that a farmer attached his hat to a string to prevent it blowing away one day, and it managed to lift off and fly for a while. Thus creating the first kite!
This country doesn't have the same extensive literary records as China, but experts believe that simple leaf kites might have been flown here even earlier than the first wooden and silk kites in China. A very simple concept, but one that apparently works. It's just a large leaf that happens to be the right shape and works nicely as a kite when correctly tethered to a line!
Later, simple fishing kites came into use through many islands near South East Asia and in the Pacific Ocean. These kites were made from leaves or bark, fastened to simple frames of twigs or reeds.