I watched and reread my documentation and I did not find this type of banner.
Its architecture does not make one think of a banner of Burgundy, but ..... I do not have all the elements.
Here are the types of flags that I found:
The banner, a large rectangular heraldic banner.
The estandart, triangular standard with images of saints, heraldic emblems and proverbs.
The oblong rectangular cornette with emblems and images of saints.
my source :
MUSEUM OF HISTORY OF BERNE
THE BURGUNDY OF THE WARS OF BURGUNDY AND WORKS OF ART OF THE COURT OF BURGUNDY
The heads of companies might have square banners, but probably with the effigy of their house