You could use the HRE warflag for switzerland. It is a red flag with a centered white cross extenting to the edges (just like the old danish naval flag).
While the cantons of the Swiss Confederation went to war flying their individual banners, they soon recognised the need for a common recognition sign, and as early as 1339 at the battle of Laupen, troops wore a long-armed narrow white linen cross stitched on their breasts, sleeves and thighs. Soon afterwards, cantonal detachment started putting this white cross on their cantonal banners. Besides its familiar bear flag, powerful Bern had a red over black guidon, and white cross on the red part of their banner became a major sign of recognition. At the battle of Arbedo in 1422 and quite regularly thereafter, mixed levies from more than one Canton carried red triangular guidons with a white cross. (from http://www.crwflags.com/fotw/flags/ch.html)