Do you have Goldstar or A65 brakedrum?
The original Flattrack GS is not made for using brake shield. The A65 is.
The rear sprockets have different par no depending on amount of teeth so it would be hard to find as it was only for these few racers.
The BB32R framed flattrack racer used the narrow chain 520 but you can use the easier to find sprocket for 530 chain.
You can use a 1965-66 A65 rear brakedrum it fits well I have that on my street legal racer that has brakes.
The 1956 Goldie "brakedrum" was bare and not used for brakes. I have one of those genuine that goes on when racing.
BSA supplied the bike with three rear sprockets 50-51-52T the gearboxsprocket was 16T from factory and narrow 520.
Have no partnumbers but check if B44/A65 rear works for you.
I believe Donelsons in Saint Louis has the sprockets
see this image, left is original 1956 flattrack never mind that the drum has extra wholes drilled or the sprocket is painted
The right is A65 1966 and I used a sprocket for 520 sprocket instead of the A65 530 widht.
Narrow 520 width ⅝" x ¼"
530 width is ⅝" x ⅜"
Oh the left cant take a brake shield with those bolt heads but the A65 1966 can..
if you use A65 parts then you can use the original bolt heads they have harder steel than the allen