A rare and unusual type of badge, which we had great difficulty in identifying. However, the RAF Museum in the UK provided the following information:
So far as I can tell this is what we call a 'sweetheart' brooch. They could be made in workshops on the station (like this example) or purchased from proper jewellers in various qualities from the cheap and cheerful to the very expensive and glitzy. The best example I have is a First World War RFC pilots wings made in white and yellow gold with diamonds and paste.
This appears to be a combination of the USAAF collar badge about 5 times larger than usual size with an RAF side cap button soldered into the centre of it. What the significance of the linkage of the two Services is, I have no idea; perhaps the chap who made it and gave it to his wife/girlfriend/mother had served in the RAF Eagle Squadrons and then transferred into the USAAF when the US eventually joined in the struggle. It's impossible to tell.
Andrew Cormack FSA
Keeper of Medals, Uniforms and Visual Arts
Royal Air Force Museum London
In very good condition, lugs intact. A unique and rare item.