Here's the stuff I've dug up. I'll be updating this as my personal testing continues:
Up Tilt Combos:
Weak Forward Up Tilt -> Up Air
Weak Forward Up Tilt -> RAR B-Air (worked at 100% on Mario)
Weak Forward Up Tilt -> N-Air (worked at 100% on Mario)
Weak Forward Up Tilt -> F-Air (worked at 100% on Mario)
F-Air Combos:
I've been messing around in the training room for about 30min and F-Air 1 really does look like the truth. Percent ranges need to be further examined but overall it seems you can get:
F-Air 1 into Jab
F-Air 1 into Grab
F-Air 1 into Up Tilt
F-Air 1 into D-Tilt
F-Air 1 into Forward Tilt
F-Air 1 into RAR B-Air (includes kill percents)
F-Air 1 into F-Smash (includes kill percents)
F-Air 1 into Dash Attack (includes kill percents)
F-Air 1 into Up Smash (includes kill percents)
And surprisingly, F-Air 2 might have hidden potential as well. True combo'ing with it is trickier but the payoff is the second hit will hold them in place rather than in the air slightly in front of you. So far these seem to be legit:
F-Air 2 into Jab (this seems far better than with F-Air 1)
F-Air 2 into Up Smash (got it to true combo on Yoshi at 140%)
F-Air 2 into Grab (could be better than F-Air 1 into Grab)
N-Air Combos:
N-Air already had some decent set up tricks in SSB4 and now will even less landing there seems to be even more potential. Depending on percents or character you can do:
Late N-Air into F-Smash
Late N-Air into Dash Attack
N-Air/Late N-Air into Grab
Late N-Air into RAR B-Air
Late N-Air into Up Smash (worked at 100%)
F-Throw Combos:
Final Cutter:
I figured out how to reliably get the 4 hit combo when doing Final Cutter -> F-Throw. Basically, once you get the 3rd hit (the descent of the blade) you gotta tilt the control stick backward to have Kirby move back when falling. This allows gives the projectile the chance hit the opponent before they hit the ground. This seems to also work in SSB4 too but the weaker spike in this game might make connecting all the hits more consistent. And the ranges appear to be far more liberal for it. For instance. Comparing Smash 3DS and Ultimate F-Throw into Final Cutter on Mario, the true combo range (for getting all the hits) in the Training Room on 3DS was about 45%-67% while on Ultimate it's about 38%-94% on Mario. The overall percent window for the combo seems to have grown about 2.5x. And since a F-Throw -> Full Final Cutter combo nets about 21% overall, it can potentially be more rewarding to do this at these percent ranges than a mere D-Throw which will only net you about 12%. That said, if you intend to do this, it's imperative that you throw immediately with no pummels. Any pummels will give opponents time to DI away which will screw up the combo.