There some WS with MND modifiers. Because of this,a Triumph Ring is actually better than a Flame Ring on those WS. Prime example of this is Guillotine.
In my opinion, this is a much better option than Flame Ring for most DD jobs (STR only modifier) because it can be use 2 level earlier, carries no penalty and can be use in Fire Resistance setup. All for a slight cost. The only job that can maximise benefit from Flame Ring's attribute is DRK wielding Scythe doing Spiral Hell & Insurgency or using Greatsword doing Spinning Slash or Ground Strike. A Taru DRK probably benefit the most.