Where to buy dust cap for bottom bracket for an old bicycle?
I highly doubt you would be able to find replacement for a bottom bracket dust cap on a bicycle which looks that old.
The economics for such parts do not make sense in general.
Something you could do, however, is 3D print it. It is a fun little project to redesign a part in 3D. You can use something like SketchUp to do it.
It will be a bit expensive though to have it printed (~tens of $), but you get to pick between different polymers.
FYI It is something I did to salvage a 1960s chest of drawers I have, where the plastic bits holding it together had become completely brittle.