I did mah research, I came onto things and this is what I found: The white flag the 7de is carrying is, indeed, the flag that was not issued until 1820. Why do they carry it? I don't know, I don't really care. They apparently based the flag on a wargame figure, how strange that may sound.
I truly think that the 7e carried a flag of 80 by 80 cm, white, with, in gold, '7e Battalion De Ligne' and 'Vive le Roi'. Why? Because none of the officers of the 7e actually spoke Dutch, and they were the ones who designed the flag (Every battalion could freely design their own), not the men. Why add something in Dutch, a language they didn't even care to learn?
Of course, that is just what I THINK. Point is, these flags:
Are not accurate. At all.