Balckflame Covenant + Archon of the Flame = ?

I was thinking on combining those but idk if they cancel out each other , while in Flame Archon you cant do Non-Fire Dmg but your Fire Dmg 100% converts to Chaos from Blackflame Covenant. Im probably turn my Dmg into Zero cause i turn every Fire Dmg into Non-Fire Dmg.

Tried it and sadly it does not work.

So it makes you deal 0 dmg?
Or how does it work with blackflame?

Im not super sure what happens to cause it but it appears you do zero damage cause its chaos damage. Even the ignite is chaos damage. According to the Archon of flame node you can only do fire damage while the buff is active.