Well, I don't think we need to spend too much more time on this. The OP is shopping this around on other militaria forums (where I am also registered) trying to find someone who will support his belief that it is a treasure. I'm seeing my own translations pop up on those forums. Tell Shinpachi-san I said "thanks for the compliment". The Wermacht Forum guys were as unimpressed with the flag as we were. It was just the poster Shimpachi on the Aviation forum who claimed it was given as a prize during a sports game, which I highly doubt. But I do confirm his reading of 体育会 as Sports Club, or could be Sports Festival, since that bit of the flag is straightened out in the other forum and is more easily visible. This would not be a natural gift to American GIs, since the patriotic slogans are essentially motivational slogans to kill enemy (US) soldiers.
Ed, we may not be experts, but we aren't stupid. Toritoribe-san and I have seen so many of these things, we know a suspicious flag when we see it.