Adding astragalus root is fine and an extra cold and flu preventative. However if you add astragalus to your elderberry syrup you should not take it during acute cold or flu as astragalus has adaptogenic qualities to it, potentially hindering the resolve of an acute infection.
This certainly limits how you can use the elderberry syrup, so that’s the only main thing I would keep in mind. Personally I prefer just elderberry, with rosehips, or star anise, or ginger, or clove, or cinnamon or a mix of all of them. They are preventative, warming and useful during acute cold or flu as well.