Modern Vespa

The UK Mods adopted the RAF Roundel.
There is also a Italian red, white and green version.
Is there a USA roundel or another USA symbol of allegiance?

Or is the roundel simply a symbol of scooter culture and pride devoid of national allegiance?

Here's the USA roundel which was used in WW1:



There's also the more well-known roundel from the WWII period:



I think the Mods chose the RAF roundel as a way of showing their love of country. I grew up in SoCal during the 1950s-'60s and perhaps someone from the UK might be able to answer the question...