Egg replacement for fried chicken
It is not necessary to have any egg to make a breading.

You should instead take a step back:  rather than trying to create a substitution for egg in  a breading which relies on their unique properties, instead use one of the many breading methods which does not.

Among them are:


Simply dredging in an acceptable starchy flour (such as corn meal)
Using a (gluten free) tempura type batter 
Using a (gluten free) beer batter without egg


All of them can be enhanced with spices or seasonings that you prefer such as chili powder, garlic powder, and so on.  The latter two can even accommodate wet prepared condiments (in reasonable quantities) like prepared mustard or soy sauce.

While the result will not be identical to the classic triple-layered French breading, it can be very good in its own right.