In the case of the breading recipe that you have mentioned, I believe that you can continue to use soy milk (or almond milk, or even water) mixed with the egg in your breading. Instead, a small change to technique should give you a thicker and crunchier coating.
You may need to increase the amount of egg/soy milk mixture you create.
Try adapting the breading method as follows:
- Dip the chicken in the egg/soy milk mixture.
- Sprinkle your flour mixture with droplets of the egg mixture, and mix so that begins to form small clumps, as if you had already been using it for many chicken pieces.
- Dredge the chicken pieces in the flour mixture again, creating a second layer with bits and clumps sticking to the chicken pieces.
This should provide a crunchier, more satisfying crust than a simple single dredge in pristine flour due to the lumps and clumps which will fry up and be crunchy and toothsome.
This advise is based on a the method described by Cooks Illustrated and Kenji Alt of Serious Eats Food lab among others. This picture is from the Food Lab article on replicating Chic-Fil-A chicken sandwiches at home: