I can’t believe I haven’t posted this yet. My go-to actually-for-real-egg-free egg substitute is Ener-G Egg Replacer. It is currently carried by Amazon.

Ener-G Egg Replacer
Their listed ingredients (but check your own box to be sure) are: Potato Starch, tapioca starch flour, leavening (calcium lactate [not derived from dairy], calcium carbonate, citric acid), sodium carboxymethylcellulose, methylcellulose.
I follow the directions on the back of the box. I always use it in baked goods, and have had luck in things like chicken nuggets as well which I wasn’t expecting.
When that’s not an option I use this recipe:
- 1 teaspoon baking powder
- 1 tablespoon water (or other liquid)
- 1 tablespoon white vinegar
The Food Allergy and Anaphylaxis Network keeps a good list of substitutes on hand as well.