My question is this- I'm working to 100 skill level in enchant and hope to get the double enchant perk. Do I NEED to destroy this item in hopes that I learn this double enchant, or when I reach 100 in enchant will I be able to make similar items without first 'learning' them??
The only way you can learn an enchantment is to destroy an item already enchanted with it. Skill level and perks do not change this. So, yes, if you want to learn the Fiery Soul enchantment to put it on other weapons of your choice, you will need to destroy that battleaxe. IIRC it's the only item in the game with that enchantment so there's no other option (barring a console command if you're on PC, assuming it's possible to "learn" new enchantments that way).
It is a really nice enchantment, though, as Chimpy indicates it's really a single enchantment with two effects - so once you have the Dual Effects perks you can put Fiery Soul on a weapon plus another enchantment of your choice and get a weapon with three different effects on it.