While we haven't personally tested this, we have a loyal reader who tried this and said that she successfully made egg free brownies with this recipe using her favorite egg substitutes. We would say that if you plan to make this a vegan brownie recipe and not use eggs to try your favorite egg replacement the first time you make them and see how they turn out.  It may be a bit of an experiment for you to find the egg replacement that you like the most to help you craft the perfect texture for your allergen friendly brownies, but you will get there.