Eggless Belgian Waffles become unbreakably hard
Flour, water, butter, and baking powder does not sound like a great egg substitute to me.

Your best option is to just go find a vegan belgian waffle recipe. There are tons of them, and they should be much more reliable than trying to modify an existing recipe.

If you're really set on modifying that one recipe, look for a better egg substitute. There are products specifically designed to act as one, as well as a fair number of other things that will likely work better than what you tried. The problem is, different ones work better in different contexts, and it can take some tweaking to get recipes to work right.