This badge gives the same buff as dragonblaze it just refreshes CD on the buff. This doesn't stack with the dragonblaze buff. Do not get this badge.
Couldn't find any information on the Eternity Soul Badge.
If you have ZERO flame damage then this is not worth it at all (still probably not worth it even if you do...)
Here's a setup with ZERO original flame damage. It only gives you +100 Flame Damage
Here's the formula:
Flame Effect = +40% Equipment Flame Damage + 100 Flame Damage