Funly enough that salute was taken from the Boy Scouts of America. I find out through history that the Nazis took a lot from the U.S. including pointers about racial segregation and Jim Crow laws.

IIRC the salute actually dates back to the Romans, and prior to its use by the Nazis was commonly known as the "Roman salute" as a result. It was so thoroughly ingrained into the Western public consciousness as a result of its prevalence in Rome that American children would display the Roman salute during the Pledge of Allegiance.

Of course, like the Swastika, its use by the Nazis thoroughly threw all of that out the window.