The best egg substitute I have found for crepes is no egg but rather time.
For crepes, I use wheat flour (white or whole wheat), salt, and a mixture of non-dairy milk and water. Mix the batter to slightly thinner than you will ultimately want, and let the batter sit for at least an hour, up to overnight in the fridge. The soaking part is extremely important as for hydrating the flour and will give the crepes better texture, flavor, and make them more coherent in the pan (important since you are leaving out eggs).
After the soak, you may need to adjust liquids by adding more water or non-dairy milk to thin to the desired consistency.
If you want to use something for the egg, you can add a tiny bit of chickpea flour (I use this for french toast), but a little goes a long way--I would suggest something like 1Tbsp per egg substituted. This can help the coherence of the batter and actually does add an eggy flavor. Chickpea flour has a tendency to clump, so I would recommend pre-mixing the chickpea flour with a small amount of water or non-dairy milk, forming a thick slurry, to get out the clumps before diluting it into the main batter.