If you're cooking something for which a fruity taste will be an enhancement, either applesauce or mashed banana will do. I've used both in baking--sometimes both at once--with good results.
However, ENER G makes a powdered culinary Egg Replacer that has no wheat, no gluten, no animal products, no preservatives, etc. and works for cooking (though it has some limitations). If your grocery story has a special foods section, this is probably where you will find it. Otherwise, you may have to seek it in a health food store or online.
Good luck in your quest.