Vegan baking and "regular" baking are two entirely different things.
First of all, there is the egg replacement, and (at least for me) it isn't always just one thing. I usually end up using a combination of things, like in this recipe where I am using applesauce to moisten and bind and apple cider vinegar and baking powder to make the donuts rise.
You also can't just swap out the flour. Coconut and almond flour are very different from spelt or wheat flour. It really makes a difference in how much liquid you need to make the batter.
In this recipe, I used a whole wheat pasty flour so that I have a little texture, but the donuts remain fluffy.
There is also no white sugar in these donuts. Instead, I've opted to use maple syrup.
I splurged and bought a donut pan to bake these, but sometimes I use my mini-waffle machine which has a donut hole griddle that I can swap out for a traditional waffle.