Yukiko is definitely about her Persona being able to act so remotely that the opponent has to block pressure even at fullscreen at times. Other than avoiding any stupid setups for being stuck in unblockables, it pretty much is knowing when you're allowed to start moving and attacking again. Most of Yukiko's attacks hit mid or low, with the only overheads being her j.D/2D (Persona drill), AoA, and j.A. With the other two only coming out in obvious situations, all you really have to do is learn to react to her relatively slow AoA and block low almost any other time.
For neutral, Yukiko can prevent overzealous approaches with her fans. You were using Chain Knuckle at good times, and I believe the SB version is projectile invulnerable. Moving in with rolls can work too, and Labrys' 5C can block out some fans if you just need some time to think or if Yukiko is tossing fans from an unsafe distance (she's got quite a bit of recovery unless she jump cancels or dash cancels them, which can only happen on hit or block).
Yukiko's Dia works wonders against crossup mixups due to the infinite vertical coverage, but the horizontal range leaves something to be desired - you can safely space B moves against to avoid the hitbox while still applying oki pressure, without really having to change up your game at all.
Uh, that's all I can think of for Yukiko at the moment lol.
As far as Kanji goes, you like... never jumped. And you got caught by a whole ton of airdives. Unlike many other matchups, grapplers can be especially abusive of even blocking, but they don't have as many options to just automagically catch escape attempts. You'll notice that trying to mash him out of stuff is liable to get you killed, though, due to his great DP and 214D grab (it has a good bit of startup, but all of it is invulnerable).
Kanji's 214 series can be avoided with backdash and jump, and can sorta be beaten by DP since Labrys' just happens to outlast the 214D startup. However, mashing any other attacks out will get caught by 214D. Between the two command grabs, 214D can be rolled behind and punished, but 214C is quick enough to catch you out of the roll due to it still being counted as a grab.
Kanji's j.214 series are more for people who jump too much. You can discourage me from overusing it (or punish Kanji players who overuse it anyway) by just crouching when I'm jumping but out of range for any of my normals. Labrys' 2B is also a pretty good way to punish up close, since it will both anti-air j.b and punish j.214 whiffs. Don't get predictable with that though, since Kanji j.C will blow you up for it.
So, jumping back and backdashing are pretty good options if you're just being free to ground command grabs, but they WILL get caught by Kanji's 5A and 5B, so don't get too reliant on those either... just use them if you're expecting a grab.
When pressuring Kanji, avoid anything that leaves a gap but keeps you close, since he can and will 214D (or, in awakening, super grab) any of those. Labrys can't really keep anything airtight after 5aa, so typically you want to jump-cancel if that gets blocked. I'm serious, 5aaa will get you punished. You can safely sweep into 214A/B and get away after that, unless sweep gets IB'd. You can occasionally mix in 214A/B without the sweep, but since it leaves a definite gap before the axe connects you'll want to use that mixup sparingly at risk of getting grabbed or DP'd.
For neutral, ground swords, 5C, and 5D can create space. 5C will discourage air-dash approaches, but it can be double jump air-dived, so don't abuse it too much. j.D can zone air approaches. Approach cautiously, since just leaping in and trying for an ambiguous crossup mixup with j.B means Kanji can just go ahead and DP you for it. Speaking of which, try having a little more patience in your attacks, as using them as soon as you're in range makes timing a DP to punish them especially simple. Empty jumps and simply waiting can be really useful.
And that's that. If you want to know anything specific, point it out and I'll try to give further advice on that.
EDIT: Also Burst Kanji's Fatal combos, they deal upwards of 4000 meterless and upwards of 5000 with meter or OMB. With command grabs being unburstable, it's also probably one of the few good times to actually use Burst against Kanji.