From 1930 to 1932, the squadron insignia of the 55th Pursuit Squadron of the 20th Pursuit Group was a yellow swastika on an blue circle that was rimmed with yellow, hence it's appearance on this Boeing P-12C.

Source (scroll to the the bottom of page four):

http://www.shaw.af.mil/shared/media/document/AFD-120530-050.pdf

While it is near impossible to look at a swastika today without thinking of Nazism, the symbol was quite commonly used by many different western militaries in the early 20th century (not to mention it's long history as an important cultural symbol). After Germany, Finland is probably the best known user of the swastika as a military symbol, as can be seen in this picture of a Finnish Messerschmitt. The Finns adopted the symbol in 1918, well before the rise of Nazism in Germany. I suppose my point is to say that having a swastika as a part of some sort of military insignia would not seem that abnormal to someone from the early 30s.

I assume you found it in the BBC article this morning? The article actually does a good job of explaining how common the swastika was pre-WWII.

In addition to /u/eightgear 's answer, it seems the US army used it on quite a lot of planes from WW1. including the Spad XIII, although the one in the picture Is a Boeing P-12/F4b. Can't find the exact squadron though, as I can't find an insignia description that has a white/light circle with a dark swastika inside.

This wiki article has a list of how the swastika was used in non-nazi nations. It appears it had strong norse links, so places like Finland stilll used it even when the world was aware of the nazi usage, shown here

Edit: plane type