What would the profile of Vulkans gauntlets be? Is it just a heavy flamesr? Or two because two hands? Or is it twin linked? Or does it have storm?

You mean the gauntlet of the Forge? Actually Vulkan He'stan wield-it. So anyone else can wield it, I guess. But if you really want, don't forgive, it's a energetic gauntlet with a heavy flamers so take a heavy flamer relic and gauntlet relic in the books and combine them. Eventually ajust the caracs. Unfortunately I don't have the Codex Space Marine so I can't help you more about that.

6th Ed codex (which is all I have to go on) says it's a gauntlet with Flamer and Digital Weapons in it.

I would agree, count it as a Master Crafted Heavy Flamer but reduce its category from Heavy to Basic which means it doesn't need bracing and isn't cumbersome. It's a relic for goodness sake! Armour wise, perhaps make it the same or similar to Artificier Armour (so 12 on the Left hand only) however I wouldn't go as far as terminator.

Additionally with the new BC/OW system, all flamethrower weapons such as this should really have the qualities of Spray and Flame as not all spraying weapons are fire based (tox guns) and not all fire weapons are spraying (fire on a stick).

Since it is also a flamer inches below your fist, I don't see why there wouldn't be any harm in using it during a fist fight if the need arose. Perhaps some rule which allows a single short burst when in hand to hand gauntlet combat. Feel free to consider this at your discretion.

Otherwise though remember that it's a Relic and could almost surely follow all the usual rules for acquiring it and (Emperor forbid) losing it.

And those be my two thrones.

I'd suggest treating it as a Pistol-class weapon rather than a Basic weapon. This lets you use it in melee or pull off some hot Gunslinger/TWW action. Pardon the pun.