As someone who has baked for years dealing with multiple food
allergies (my own and others) I have used flax seed with great
results. (I sent you a private email with the substitution: 1 tbsp
flax seed freshly ground + 3 tbsp water for each egg)
I researched seed allergies and found this:
http://www.allergy.org.nz/about+allergies/food+allergy/seed+allergy.html
which states that linseed allergies are rare (the main component of
flax seeds)

However, pectin is also a great binder. I use grated apples in some
recipes but I doubt you want your matzoh to taste like apple! You can
buy pectin most places. Another choice would be gums: I prefer guar
gum for the lack of after taste.

As for a flour substitute, I find tapioca flour to be the best for
giving the right mout feel to breads and baked goods.

I personally haven'y experiment with matzoh balls yet for the perfect
recipe as I have gained so much weight this year dealing with a hip
injury that has limited my activities so I'm keeping my carb intake to
a minimum.
But that's on the list for post surgical recovery so I'll make sure to
post the winning recipe!

Wishing you luck!

L'Shana Tova to all!

-kim