I heard a few times Vivec had armor. Of course from what I see, his features look like he has armor on but is there armor you can loot?

Vivec has no lootable armor (other than a second wraithgaurd, that still must be taken to the dwarf, that is used as a backdoor if you kill him before you get the real wraithguard). I'm sure in times of war he would wear some armor, although in his state now (yadayada CHIM yadayada God), that he would find little use for it.

And to add to the top post, I would say he would just wear the armor parts just to look cool rather then it functionality.

Well, he kind of looks like he's wearing some type of netch pouldruns.

I believe that one side of him wears chitin and the other side bonemold.

That is correct, in fact, since Vivec is, according to the game mechanics, considered a "creature" rather than a "humanoid", he can't wear armor, his pauldrons, as well as that loincloth, are part of his model and not actual items that exist in game tersm (would you want to take his loincloth anyway, though? Do you want to see Muatra that much?), I think I recall one replacement mod for Vivec's model including an optional esp that gives him lootable armor, but by default, it is not lootable.

And yes, if he did wear armor, it would probably be more cosmetic than functional, I don't think you really have much need for armor when you're a god. And the pauldrons he has on now seem mostly cosmeic too, I mean, they don't even really cover much of his shoulder, armor isn't going to do anything if it leaves much of your body exposed, at least not normal armor, maybe Vivec could use his god powers to make armor that looks like it only protects his shoulders protect all of him, not that he would need to.