Further googling led me to the Cross of Burgundy, shown below,
and this reference to Scottish soldiers:
Pedro de Ayala, writing in the 1490s, claims it was first adopted by a previous Duke of Burgundy to honour his Scottish soldiers....However, earlier chronicle accounts and archaeological finds of heraldic badges from Paris indicate... its origins are more likely to relate to the fact that St. Andrew was the patron saint of the dukes of Burgundy.
I have found references to a white cross on various backgrounds (red, sky blue, sage green) but nothing (other than Reinel's map and the apparently mistaken reference to Scottish soldiers above) relating to a red cross on a white background.
I'm wondering if this red on white representation is based on any evidence of actual use in Scotland, or if it is an error made by Pedro Reinel. Did he perhaps get it mixed up with the flag of St. George?