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The Flame Shield is a nice upgrade over the Silver Shield, providing an additional 4 Absorb as well as resistance to Cold. This resistance won't help within Gurgu Volcano where the shield is found (though it grants no weakness to Fire), but can help against the FrWOLVES and Frost Ds in the Ice Cave. After the Class upgrade, the Flame Shield and Ice Shield are the best shields that can be used by your NINJA.
The Flame Sword is not nearly as powerful as the Ice Sword found in Gurgu Volcano, making it pretty useless as a primary Weapon. If elemental Weapons actually worked in the NES version of the game, it would have some use, but instead it's a potential RedMAGE Weapon at best.
The ORB of Fire
Page
4
Description
Armor forged with the essence of fire.
Type
Armor
Absorb
34
Evade Penalty
−10%
Value
15,000 gil (15,000 gil on Easy)
Found In
Mt. Gulg B5
The Flame Mail offers the same Defense as the Knight's Armor, but with significantly less of an Evasion penalty, and a bonus resistance to Ice (though the Flame Shield already grants the same resistance). This and the Ice Armor are the best body pieces Ninjas can wear. Try giving non-matching elemental Armor and shields to your Ninja to maximize his elemental resistances.
Defense
29
Evasion
−33%
Type
Body
Magic Def.
+5%
Magic Penalty
58%
Value
5,000 gil
Found In
Castle Fynn Basement B4, Mysidian Tower 3F
Dropped By
Fire Gigas
For some reason, even though the Flame Shield resists Ice, the Flame Armor resists Fire (the Ice equipment has the same strange relationship with its Shield). The Flame Armor is also a nice upgrade over the Knight's Armor, adding 7 defense. It also reduces your evasion by a like amount, but by this point your shield skill should be high enough to compensate for the loss.