Before I talked about master’s who specifically called for parrying with the edge. Now here are some passages where the flat is used.
So you are fighting someone with the falchion: if he strikes you, deflect it to the side with your falchion with your flat and on your crossguard; go quickly forward with your left foot and hit him with the pommel in his arm, as shown here, so that you strike him on the head.
— Zabinski’s Translation of Codex Wallerstein, plate 57, page 124
Next, when anyone strikes down at your head: deflect with your flat and on your crossguard; push his falchion to the side so that he has to strike; and when he wants to strike, find the openings and chop his arm off, as depicted here.
— plate 61, page 124
Keep in mind that other passages in Codex Wallerstein call for parrying with the edge.