Here is a method we used for a vegan cake it worked out beautifully!

To replace one egg:
1/3 cup water
1 tablespoon whole flaxseed
Place the water and flaxseed in a pan, and bring to a boil. Lower the heat and simmer, watching closely as the mixture thickens to a gel (about 5 minutes). Remove the pan from the heat before the mixture gets too thick and gummy. The flaxseeds don't need to be removed from the gel.
-- The Allergy Self-Help Cookbook by Marjorie Hurt Jones, R.N.

Thanks for sharing. Will certainly have to try that.