According to this page, which cited a study of Air's ending:
From: "Colourful Pure Girl" in the March edition.
"The author declared that those two kids were not the reincarnation of any of the characters and he doesn't want people think of air like that."
The author also says that those two kids were more of outsider view point. It's like themselves (KEY) are watching the story.
How to get to the study's page:
(The text is taken from Key Fans Club.)
In more detail: the study said there were three curses that were cast on Kanna:
Restriction on reincarnation. This was the direct result of the sealing a thousand years ago, and the effect was that in a set period of time, Kanna's soul could not be reincarnated. This curse was automatically lifted after about a hundred years when the power of the seal had weakened.
Solitude. This curse was an indirect effect of the sealing of Kanna, caused by Kanna's sadness and guilt over Ryuuya's death such that she became unable to form a close relationship with anyone lest she suffered great pain. This curse was lifted by the development of a close bond between Misuzu and her aunt, Haruko, made possible because of Yukito's sacrifice, which prolonged Misuzu's life by temporarily saving her from dying by the third curse.
Dreams. Dreams were the manifestation of the memories of the winged beings in their reincarnated bodies. Both the vastness and accumulated sadness of the memories of the winged beings could damage a human's body. Yukito offered his mental storage capacity to Misuzu so that she would be able to live long enough to break the second curse, which prompted his own memories to be transferred to Sora. With the second curse gone, Sora flew to the heavens to bring the last happy memories of Misuzu to Kanna so that she could be released from Ryuuya's shadow and returned to Earth, and blend the memories of the winged beings with the Earth's. From then on, no one needed to bear the memories of the winged beings alone anymore, so the third curse was also lifted.
The children playing on the beach at the end should not be seen as the reincarnations of Misuzu-Kanna/Yukito-Ryuuya, but as the all-knowing Key staff and you, the viewers.