Thread size is 3/16 cycle, the nearest you will find modern equivalent is 32 10 UNF, same old 55/60 degree angle difference. I got some NOS from Russells not long ago.
Yes quite difficult to find those 3/16 x 32. If you buy chaincase screws from most sellers now they will just give you 2BA as the nearest equivalent. I've used stainless 2BA in all my BSA's and bead blasted the heads for a cad plated look. Ron