I have a lot of Kobold Press material. I love the Midgard Campaign Setting, but unfortunately, I haven't had much of a chance to use the setting itself. Currently, it's easier for me to use a published adventure set in the Realms than to build a campaign from the ground up. Not only do I have the structure already in place with the adventure, but decades of being a Realms fan (and 5th edition hitting the reset button a bit) have made it easy enough for me to act like I know what I'm doing with less prep time.
That said, as I look through the Kobold Press library that I have, I can see a lot of potential for people that might be running Storm King's Thunder to insert some "Kobold Enhancements." So I'm just going to call out a few items from a couple of products that could be used to reinforce the themes of the adventure.
And before you go any further, there will be some spoilers for Storm King's Thunder in this post.
First off, Giants are noted in Volo's Guide to Monsters as being more likely to learn rune magic than to dabble with the arcane traditions of wizardry, with the exception of Cloud and Storm Giants. Stone Giants are exceptionally versed with rune magic. The only problem is, rune magic isn't really a thing in 5th edition as of this writing. There are a few magic items in the adventure that play with runes in an interesting way, but that's assuming that giants make the runic items "offscreen."
Thankfully, Kobold Press has a 5th edition compatible product that is all about rune magic, Deep Magic--Rune Magic. In fact, right at the beginning of the product it mentions that some monsters might be attuned to certain runes and gain the benefits of the feats contained in the product for runes especially appropriate to their nature.
Some of the Giant leaders are essentially normal giants of their type with a few more hit points thrown into the mix. Giving some of the giant leaders access to appropriate runes is a way to make them stand out even more than the added durability of extra hit points. There are runes grant those who understand it's power additional radiant damage, granted by their gods, the ability to control weather, extra lightning damage and a strength bonus, and a host of other effects that would make sense for various Giant leaders.
Suggested Runes for Giant Types
Stone--Algiz, Ansuz, Berkanan, Eiwaz, Fehu, Gebu, Jera, Naudiz, Nykoping, Wunjo
Frost--Fehu, Hagalaz, Isaz, Raido, Tewaz, Turisaz
Fire--Ingwaz, Kaunen, Otalan, Sowilo, Turisaz
Cloud--Ansuz, Berkanan, Dagaz, Gebu, Hagalaz, Isaz, Jera, Naudiz, Nykoping, Otalan, Perto, Sowilo, Turisaz, Wunjo
Storm--Ansuz, Berkanan, Dagaz, Eiwaz, Gebu, Hagalaz, Ingwaz, Isaz, Jera, Laukaz, Mannaz, Naudiz, Nykoping, Otalan, Raido, Tewaz, Turisaz, Wunjo
Tome of Beast Substitutions
I love D&D monsters, but let's face it, some of them get used for similar roles a lot. On top of that, it's just fun to throw in new monsters once in a while. The Tome of Beasts has lots and lots of new monsters.
If you, like me, have seen a veritable legion of bugbears since running 5th edition D&D, you might consider substituting the Ratfolk Rogue from the Tome of Beasts for a few of them. Sneaky ambushers, and nothing about them makes them seem incompatible with the other monsters in Faerun (assuming you are running Storm King's Thunder in the Realms). Standard Ratfolk can stand in for goblins, and closer to the colder regions, the Fraughashar can stand in for Hobgoblins. Replacing goblins, hobgoblins, and bugbears with animal folk and fey creatures also gives the adventure a slightly more fairy tale feel to it.
Giant-kin in the Realms (creatures with the giant type that aren't Hill, Stone, Frost, Fire, Cloud, or Storm Giants) are considered the bastard offspring of Annam's wife Othea, and they don't get treated very well by True Giants. Because of this, lots of Giant-kin could be pressed into service of evil giants, and either swapped out for some of the encounters in the Giant lairs, or added into random encounters as the player characters move across the North. Forest Marauders, Lake Trolls, and Trollkin Reavers all work in this capacity, as does the Corrupted Ogre Chieftain in Appendix A.
The Hunt Lords at Noanar's Hold are described as wights that ride warhorse skeletons, but the Ghost Knight in Appendix A of the Tome of Beasts is ready made for the description given for the Hunt Lords.
If the player characters accept the dragon Klauth's offer of the cultist crewed airship, the cultists don't have much personality, as presented. While the GM could work to add some individual personalities, it might also be worth it to leave the cultists as the "straight men" on the ship, and add in an Ash Drake or a Crimson Drake, who act as Klauth's supervisor among the cultists. The smaller creatures can get comically overblown egos as they boss around the crew or even butt heads with the PCs throughout their travels.
The original Twilight Giants novels included a rank in the Ordening above even the Storm Giants, that being the Titans, although the Titans weren't terrestrial dwelling giants. While the main adventure doesn't mention the Titans (probably because Titans got a bit confusing between 4th edition and previous editions--the Monster Manual even calls traditional titans Empyreans instead of Titans), it can easily be reintroduced into the storyline. Titans could have been cast out of their celestial homes as well, which gives the GM an excuse to use the Degenerate Titans from the Tome of Beasts.
Flab Giants can be introduced as simply fatter, less active Hill Giants, and they fit the theme of Hill Giants and consumption. Desert Giants fit the broad thematic tone of most of the "classic" true giants. While the Jotun presented in the Tome of Beasts are a bit outside of the scope of the adventure, Thursir Giants could easily be Giant-kin that are pressed into service by the other Giant types, especially the Frost Giants, who avoid forgework themselves due to the heat.
Also--this adventure is in the North. Lots of mountains. Potentially lots of snow. Find a way to use Bearfolk. I don't care how. Bearfolk are awesome.
Anyway, even if you aren't using Kobold Press' really awesome campaign setting, it might be worth it to look into some of their products if you want to swap out the more commonplace elements with something new, but still appropriately thematic.