What are "rye sours"?
The King Arthur website lists the ingredients for that item:
http://www.kingarthurflour.com/shop-img/labels/1416587131567.pdf

It looks like the "sour" flavor comes from several acids (acetic, lactic, and citric). I assume the recipe calls for "sour" flavor instead of being a sourdough recipe like a traditional rye bread would be. Pickle juice may be a good substitute, since it's mainly vinegar [i.e. acetic acid]. The "bread improver" also includes wheat gluten, which may be helpful if you're using a non-bread flour (bread flour contains more gluten than whole wheat or AP flours).