NEEDED- Vegan NOODLE recipe (for pasta maker)

I need a basic vegan noodle recipe. Like the kind that could be made in a pasta maker (or more specifically, the Omega juicer's pasta attachment). I know regular pasta uses eggs, would I be able to supplement ground flax as the "egg replacer" or what else could I use as a NATURAL binder (none of the who knows what it is egg replacers at the store, this is for my sensitive parrot)? Also, would I be able to use alternative flours, such as rice, buckwheat or nut flours? I am looking to make a special treat for my bird