I haven't tried it myself but one of the readers mentioned in the comments that she used rice flour instead of all-purpose flour and a little bit of extra soy milk and the bread turned out fine. Most of the gluten-free and egg free recipes use Xanathan gum for it to rise. I haven't tried Xanathan gum while baking. The reader mentioned that she didn't use it either and the bread turned out good.
Egg Substitute 101
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