ooh! kaos happens to be one of my favorite characters, and you bringing up him being a dark portal master... I do not own every piece of skylanders media, but I will do my best to summarize his skills in a detailed manner.
within spyros adventure. he has control over various elemental spells, which range from doom sharks to lasers, his mechanical suit also utilizes these spells and I assume them to be built into the suit, he also seems to be able to summon his minions at free will. its never stated whether his giant floating head is via technology or something else, the closest we get is him telling glumshanks to turn it off after trailing off.
in giants. the only skills hes seen using are directly connected to the iron fist (summoning arkeyans, eye lasers, the healing-damage-spell contraption), though I do not know much of it is due to the iron fist or his own built in magic.
swap force, in VV nature, features a different set of capabilities for him. he uses petrified fire in one cutscene without any prior build up, and as super evil kaos can create shockwaves or bring his thoughts to reality. I must say that I was... unimpressed, back when I saw he didnt use anything relating to petrified darkness... but I am getting off topic.
trap team, which was of course done by TFB, gives him a new super powered form. when affected by the stinkocity, he appears to... be able to see through dimensions? as he can see you (the player) through the tv screen, his vision also became faux psychedelic which I feel is relevant enough to mention. as his traptanium form he sprouts wings, gets crystal blades, can make... black energy? I dont know how to describe it, amongst some other things.
superchargers has an interesting spin... which I quite like! he seems to be getting a power boost from the darkness, and actually utilizes some of his own spells (to my understanding, I am unsure if its been confirmed anywhere), such as teleportation + fake copies, crystal swords and hands. I think this is a really wonderful change of pace compared to his usual per-game super powered form.
imaginators, I feel is the weakest. he lost his connection to the darkness after it was destroyed in superchargers, so instead we get mind magic and... super saiyan final boss...? imaginators is an extremely short and unfinished game to my knowledge, so I will not dwell on it for too long, but I believe mind magic lets him imagine anything into existence. though you can argue its not actually him whos using the magic as I believe it comes from brain.
its extremely easy to make a joke about kaos only being a threat when he has outside forces assisting him, but to me that is a massive disservice to his character.
it has been a bit since I read the novels, but in those he uses a wide variety of spells from teleporting individuals with the snap of his fingers, lightning, flying flower pots, lightning that drains your energy, as well as various contraptions like a miniature portal. the novels have a strange habit of switching back and forth from him being a threat and a joke, but the skylanders rarely face him head on due to him backing them into corners with his own skills & tactics, which I enjoy! upon acquiring the mask of power, he can steal the skylanders powers, though I feel this is unnecessary to further go into.
one thing interesting about kaos is that he is extremely tactical while being horribly impulsive, so he ends up in a strange situation where he has the cards to win, but his emotions get the better of him. he is also someone who uses a lot of technology in his plans, and its not uncommon to see his spells accompanied by a contraption, that is typically implied to be created by him (or, that is how I have always seen it), he also created & brought the wilikin to life as a young portal master.
I am sure there are pieces I have missed, due to not owning every book. but if so those who own those books can likely provide.