This thread is alittle old but I found it attempting to solve my own issue of finding some headbadge screws. They are 2-56 thread size (if you didn't know that already) and I got some at Fastenal for like .06 cents a piece(they had to order them so they ended up being $1). They are not flatheads though but phillips head, but the headsize is comparable to the original. They are also stainless so they polish up nicely. You probably can get the same at Grainger or a fastener store.
Also, if you want to use small schwinn style headbadge screws on a bike that doesnt have the holes already drilled and tapped. I got the tap off Amazon (yes Amazon :roll: ) for like 4 bucks+ the ride. It was miracle that I didnt break it.