I don't think Flying Scot is connected in any way with the Scott motorcycle. One of the models that Scott made was called the Flying Squirrel. Incidentally, that S-A item on Ebay looks like a motorcycle gearbox end cover. The clutch operating arm is just to the right of the S-A logo. Sturmey Archer made gearboxes and complete engines used in pre-WW2 Raleigh and Dunelt motorcycles, among others. A lot of cross pollination between bicycles and motorcycles years ago.
Best Regards,
Wes Gadd