Jab - this is sounding like possibly the best heavyweight Jab in the game. Starting at frame 4 and dealing 12% damage is crazy. It's largely the same as Charizard's from Smash 4, which is nothing to sniff at. Excellent boxing move for opponents who get close.
Forward Tilt - This sounds worrisome at frame 12, but you shouldn't be looking at this the same way as the Jab, as it has a different purpose. With armour and decent kill power, this serves too functions - to kill when a normal smash is too slow, and to armour through oncoming attacks. A comparable move is Little Mac's Forward Smash, which is obviously stronger but 2 frames slower.
Up Tilt - This is insanely fast, coming out at frame 5 - that's the same as Mario in Smash 4! It's got a big hitbox too, so looks to be a great anti-air attack.
Down Tilt - This is frame 14, so the slowest tilt, but you should bear in mind it's on par with Mario's Forward Smash - remember how hard that is to react to? This move is for the utility; it's got deceptive range and if you get a bury off of it you've likely got a KO at any reasonable percent.
Dash Attack - frame 7 (same as ROB - that's fast!), armour and a lot of damage makes this a strong burst / kill option in a similar vein to forward tilt. I think this is a more aggressive option for attacking opponents hiding behind hitboxes, whereas F-Tilt feels like a more defensive move for when you're under assault, so both have their uses.
Forward Smash - This is slow, but goodness is it strong. Not a smash attack to just throw out, but excellent kill option on buried opponents with a lot of range. Let's also remember that frame 19 is not as slow as you think it might be - that's the same as Captain Falcon in Smash 4, for example, and it looks a lot stronger.
Up Smash - This is an incredibly weird move with a lot of different uses. It has an absurdly fast first crown hitbox on frame 6, which may be a very potent anti-air or burial punish. It then has a spiking hitbox, so may have weird edge=guarding potential. I don't really know what to make of this, to be honest.
Down Smash - At frame 24, this is relatively slow, but don't let that distract you from the fact that it has super armour. This is going to be incredibly strong for hitting opponents who don't sweetspot the ledge.
Forward Throw - This is perhaps the most unclear move for K Rool in terms of its usability. It's not his most damaging, nor does it look like a kill throw, but I've heard rumblings of whether it can be used to combo. We'll see.
Back Throw - the Pushblock video suggests this might be a kill throw! I've not yet seen footage, but that sounds promising as well.
Up Throw - This looks like the most damaging throw in the entire game, with relatively low base knockback that may make it useful for low percent combos whilst allowing it to kill on platform stages.
Down Throw - This buries off of a grab - letting K Rool do whatever he wants after. The exact utility is yet to be discovered - you can mash out quickly - but at high percents this should be a guaranteed smash attack kill.
Neutral Air - This is Dedede's, but with larger range and super armour at the expense of a single frame. This is a really strong tool for escaping juggling that no other heavy looks to have.
Forward Air - This is a relatively fast (frame 10) killing aerial. I think our first job collectively should be to try figure out ways of linking into this from burials, because it's a really strong move.
Back Air - At frame 19, this is very slow, but does a crazy 19 damage with a really cool spike. Worth looking into its use after burials, because you apparently can't tech grounded spikes anymore.
Up Air - Frame 7 is very quick here, with a lot of kill power and a potential disjoint. We should investigate down throw up air as a potential option.
Down Air - same deal as back air, but a lot quicker. This should be the go to spike without trying to style.
Neutral B - This move does everything thanks to the confirmation we don't need to fire a cannonball to use the vacuum. It gives us a projectile to approach behind, a command grab to give true aerial pressure on shields, and an option to absorb other opponents projectiles.
Side B - This move looks to be as fast as Link's boomerang, and should serve a similar purpose of controlling space and forcing shields so that we can land those grabs. And it has super armour, for some reason....
Down B - K Rool has nearly everything, so you might as well throw in a counter as a potentially decent option for escaping disadvantage, as well as a good option for edgeguarding opponents with damaging recoveries.
Up B - Yeah, this is crazy good. Goes faster and farther than Duck Hunt, with a hitbox on top that messes with anyone who wants to spike or 2-frame you? This recovery is absurd.