From actual birch sap, or from flavoring in a jar?
AFAIK, the actual birch sap has to be tapped from Betula lenta "cherry birch" (NOT white birch or paper birch--only cherry birch has the right wintergreen-y taste) trees in early spring, then boiled down like maple syrup, except you have to boil it 100:1 instead of 40:1. Then you'd just mix that with fizzy water and red food coloring to taste.
It can be made with extract, obviously, but danged if I can find a source for real birch extract. Even the internet is failing me...