Listen:
Dual hoj (colossus sword for dmg and range) + dragon (without sinergies add 750 weapon dmg and aura is few hundreds)
Hellwarden's Will (help for ias ww breakpoint & fire res malus)
Horazon boot + gloves (cbf + 40frw & boost fire damage + 30ias)
Rings: fire opal + rare with dual leach
Amu: highlord if need more ias.
Belt: dungo?
With this set up you can reach max ww attack speed with -60 fire res.
But idk. Probably the lack of a natural sinergies makes this build awful also idk how many times i have to repair the swords cuz i always played ww with PB or botd
Definitely works! I would personally just use PB because of not needing to repair, but I get the CS range argument.
I think your build would do a TON of damage, and was the first thought I had for how to do it because the aura adding ~1k to each WW hit is pretty serious business. The only problem (and the reason I went with phoenix in my reply) is that it will freeze your targets, rendering them unhorkable. There's also no teleport, which obviously hurts the utility of any character unfortunately.
I would do a couple of things a little differently if I were leaning into the lack of teleport. As the vast majority of the damage is from the fire, speed is all that matters. I would 10000% be using PBs just for that reason alone. That way Highlord's and gloves get you to the 3 frame breakpoint, which is where most of the damage difference between the phoenix/hoj builds comes from. This opens up some fun things like using just a 3 open socket barb helm with the skills you like, like finding one with increased speed and natural resistances to save some hard points, and filling them with +20/-20 worth of facets + defender, which will add a crazy amount of damage. Or a jeweler's diadem with something like 30% FRW to lean into that part.
At the end of the day, the reason to run a barb like this is if you have someone to enchant you. And that enchant damage boost is way more than any fire aura can add, so you want to lean into what helps you apply that damage, which is fire penetration, attack speed, and, honestly, teleport.
If you want to not teleport, the following does about 20k more DPS to fire immune p8 tz96 super uniques (like Geleb). Dual phoenix, jeweler's helm with +20/-20, jeweler's armor with +10/-10 and 2 15% IAS jewels, horazon gloves/boots, SOE, mana leech ring, highlord's, and a -10% sunder. Without charms it will kill everyone in the council in a second or less.
You're right in that without the synergies, there's no real benefit to the auras. But because the barb is able to deliver the damage so many times and so fast with WW, it can make up for it if there's enough penetration. This character with a good enchant would blow any fireball sorc away.