I know you've probably already made the cake but I just wanted to answer your question and say that
as of now I don't
recommend flax meal
egg replacers in cakes, due to it not being a structure builder.
Finding substitutes, especially for
eggs, has proven to be a continuous challenge
as I can also not have store bought
egg replacers, flax seeds, tofu, potato, or yogurt... all of which are commonly
recommended egg substitutes.