Traditionally green, rough sawn red oak was used under many types of roofing. It's very difficult to drive a copper nail (even a common nail) straight in fully dried oak. Over a year or two the the green oak dries and clenches the nail shank creating a much higher pull-out value.
This is unnecessary and is no longed standard practice. We have the famous Peach Bottom slate local and it's always installed on plywood with large headed copper or stainless nails. There is no reason why you couldn't use stainless or hot dipped galvanized screws,(not electro plated) right on your framing if spaced close enough.
Fire-rated plywood is available but it's OK with code to paint the ply with
Fire and Flame Retardant Paint and it's cheaper. You could then use underlayment (30lbs felt paper) and keep all precipitation out. Slate on lathe will admit a some moisture when it's wind driven.
You could most likely achieve decent pull out values with stainless deck screws driven into the cement board as long as it's not too windy at your oven location. If that's a concern use 2 layers of board and I think you'll be fine. You could also apply a polyurethane construction adhesive to the undersides as well and that would be bullet-proof.
Mark