The one use I can think of is my favorite. Use it as a flamethrower to deal with any annoying mob that gets in your way. Cooked pigs will drop Cooked Porkchops, and barbecued cows will drop Steak. Hold down the right mouse button and it shoots fire. It is also used for destroying wood quickly. The Wand of Fire can only be used for torching mobs and people, as far as I know.
Crafting will cost you 75 Vis, along with one Enchanted Wood and a Fiery Crystal in the Thaumic Infuser. There is no set crafting arrangement to make this item, rather, one may simply put the required materials in any of the 3 slots of the outermost triangle.