Ummm, you -are- aware, aren't you, that those children are indeed pledging allegiance to the American Flag, and that in the timeframe of the photo (late 1800's) that was a perfectly valid way for an American to address the flag?
That's the form of salute used by the author of the Pledge (Francis Bellamy).
40 years later it was changed by FDR because it looked too much like a Nazi salute. But the American one came first.