What is a dairy free substitute for buttermilk when making fried chicken? Just use egg?

Why not take rice - and boil it to a creamy consistency? I think that would work well.

I soak my chicken pieces in coconut milk for 30 min.

You can skip the milk and the egg, and just dredge the chicken in flour, salt and pepper. Let the dredged chicken sit for 10 minutes and then dredge again (double-dredging.) If you are pan frying the chicken, make sure the oil/shortening is hot enough before you put the chicken in the pan.

Soy milk with a little lemon and vinegar should work fine. If you are soaking it you might need to soak it a little longer. If just adding to a recipe you'll be fine. Good luck