Does the extra 1d6 fire damage to “grasped” weapons granted by the Gauntlets of Flaming Fury effect the Thunder Gauntlets from the Armorer Artificer subclass if the Gauntlets of Flaming Fury are the Thunder Gauntlets?
Not as written
The wording for Thunder Gauntlets that are a part of the Armorer Alchemist's Guardian Armor model state:
Each of the armor’s gauntlets counts as a simple melee weapon while you aren’t holding anything in it and it deals 1d8 thunder damage on a hit.
The "and it deals 1d8 thunder damage" clause only applies when the gauntlets are used as simple melee weapons, which they only count as when no other items (not just weapons) are held.
So as soon as the Alchemist holds anything in a hand, that hand's gauntlet can't benefit from Thunder Gauntlet.
Meanwhile, Gauntlets of Flaming Fury from Baldur's Gate: Descent into Avernus state:
While you wear both of these steel gauntlets, any non-magical weapon you grasp with either gauntlet is treated as a magic weapon. As a bonus action, you can use the gauntlets to cause magical flames to envelop one or two melee weapons in your grasp. Each flaming weapon deals an extra 1d6 fire damage on a hit.
So the Gauntlets essentially ignite whatever weapon they are being used to hold. However, because Thunder Gauntlets require that the Alchemist not be holding anything in them, you have an either-or, but not both situation.
User Medix points out that it is possible to bring this whole issue to a grinding halt even before this. The line of reasoning goes something like this:
Armor Model's Thunder Gauntlets relates to the Arcane Armor feature. That feature states:
As an action, you can turn a suit of armor you are wearing into Arcane Armor
It is possible to parse this to mean that only complete suits of armor may be made into Arcane Armor. If part of that suit is replaced, the replaced component is not able to benefit from any features of Arcane Armor that the part it replaced could benefit from.
In other words, because Gauntlets of Flaming Fury are standalone gauntlets and not part of a larger suit of armor, they can't be used with with any gauntlet-related features of Arcane Armor.
I personally think that puts players in a terrible position where they have to choose between class features and magic items. Magic items are meant to be attractive character upgrades.
Moreover, the rules for Arcane armor state "Your metallurgical pursuits have led to you making armor a conduit for your magic" I think that's sufficient textual support for a DM to rule that an Artificer is clever enough to figure out how to incorporate magical armor into a larger suit. As Tim Gunn might say: Make it work, Artificers.
I feel like it should work, because the gauntlets say that they cause magical flames to envelop one or two melee weapons in your grasp (as opposed to a weapon your holding with the gauntlet) and because when you make a fist the thunder gauntlets are themselves in your grasp of your actual fleshy hands. If the gauntlets specified that they worked on a weapon that you’re holding with the gauntlet, then I could see how it wouldn’t work.