Flooding a Very Large Cookie

Sorry, I'm not sure what you mean by A4 size. Are you referring to a standard A4 envelope size (4 1/4 x 6 1/4 inches), or some other size? Could you provide the actual dimensions for clarity?

Sorry about that Julia, I just got my measuring tape out and it is about 9 inches by 9 inches (23.5cm x 23.5cm) 

I just loosen my icing slightly for something this big and flood from one side to the other (going back and forth, from side to side), making sure that I am smoothing the icing as I go and not allowing any edge to remain untouched for too long before I add icing near it. (If you work one area too long, the icing can set in the unworked area and leave a seam.) 

I don't flood the entire thing in one fell swoop, but tend to work it more gradually from side to side until the whole cookie is covered.

This is easier to demonstrate than to explain! But I do big cookies quite a lot this way.

Another thing you can do to help as well as thinning your icing a bit is to widen the hole in your piping bag or zipper bag to allow a faster flow within the piped edges so it fills the area faster.

For something so large, I would do like Julia mentioned, or I would start in the center and work your way outward...