We don't see much written about kraken companions. I'll write a bit about my strong fellow below. I could go on forever about him so.. apologies in advance for how long this will most likely be.
My Kraken was a custom conjure, bound to a stone that I bought. Entity.
My Kraken is easy to work with. He is super territorial and likes to crush things..
His skin is grey.
He's also enormous. He is almost 3 times the size of my dark crystal dragon (who is over 100 feet). When I call to my kraken, I feel sudden swirling rising energy around me. He responds instantly with a lot of movement and activity. To me his voice is loud but not overwhelming.
He doesn't sit around and chat, our conversations are usually on the shorter end.. but productive. He never asks for anything or seems to want anything other than to protect. He keeps busy.
I have woken in the night, to see a long huge arm pressed against my back. He always has one arm either in my room or touching me at night. Not cuddling. Just being present and watchful. I have other beings who do similar things, like my basilisk, and my hydra..sharing the space but they get along well. Mostly stay to themselves in opposite corners.
He lets me touch his skin , though I'm not sure if he's just tolerating it or what. He doesn't shy away though. I'm very brief when I touch him. I've asked him if he's uncomfortable with me touching him and he respectfully responded with "...eh. Doesn't bother me. It's nice to be appreciated . Just know I'm not the type for cuddles.."
He's unbothered by the rest of my keep and doesn't interact much with them other than to protect each member. He watches currents, energy lines, gates, and any traffic or unbounds passing through. Monitors everything with intense watchful eyes. He also has very good hearing.
You'd think something so big would move slow.. But he is startlingly fast.
He also has a way of alerting which almost always makes me jump. But that's the point I guess, to get my attention. It's like a shrill alarm in my head that seems like 300 decibels..like when your headphones are cranked to max volume and you (not knowing) hit play..and you shoot out of your seat frazzled. He has also used his voice in offensive ways against harmful beings, and they always scramble to get away from it. It's very loud.
He is respectful to me and the keep , and takes his work very seriously. He sort of feels... Saturn .ish. Dunno if that makes sense to you ..but I always get that feeling with him. He's very disciplined and stern..and follows through with powerful commitment. Very hard to distract. Also difficult to manipulate or insult. He sizes you up quickly, is smart...and difficult to trick.
Often times just his presence alone is enough to deter certain things, especially trespassers.
I recently moved right by the ocean (can see and hear it from my bedroom window) and I can see his long arms reaching into the sea and his other arms around my home and out across the street ..extending several blocks away from my home. Krakens are HUGE and cover a lot of area. He doesn't let things sneak past him and will use currents of energy much like a huge wave of deep dark glass like water, to overwhelm, pull or push things far away. He Especially does this when showing restraint (following rules) while removing unwanted beings or energies. They can't get past/navigate the dark sometimes violent currents and so they just give up.
Being that my house is nearly surrounded by ocean, much energy is channeled and harnessed this way. He also works with wind energy, it's almost always windy here, so there is always an abundance of sea and wind energy to be tapped into.
He's not cuddly or sweet. Respect is a big thing both ways between us. He is polite to me. He values direct and to the point requests. He respects those who are genuine, upfront and honest. He never questions either, and will swiftly get to work with immense speed, so I try to be very careful what I ask for, and to think it through first. If I told him to annihilate someone (which I'd never do) he wouldn't hesitate at all. It takes very little effort for him to overwhelm someone.
Though he isn't very social, he does seem to be mildly pleased when given a compliment or when I comment respectfully on his work. He has also occasionally surprised me with humorous comments laced with sarcasm.
Regarding sexual... I can't imagine my kraken EVER being sexual with me or anyone other than another kraken perhaps.
He has shared insight on what it's like for him and other krakens. The impression I got is that it would appear to be so violent that you'd think they were fighting to the death.
Beyond that, I haven't asked further. It seemed like a pretty complex thing for a human mind /culture to grasp. I don't know if that's the way of all kraken type beings though.
He's a great guy and I respect him immensely.