Hello, I'm Polkadog and this is a summary of my play style as Hybrid/On-Hit Kayle.
I'll be explaining why, when, and when not should you play H/O-H Kayle.

Hybrid/On-Hit Kayle is a play style that is really really versatile and made for balancing the teams, yours, and the enemies. The 2 main items in this build are Nashor's and Rageblade. Riftmaker is overall the best Mythic for Kayle so we'll keep that for now.
Nashor is the most commonly built AP item on Kayle due to the massive amount of AP and MS it provides, both things that Kayle wants. The On-Hit effect of Nashor also provides really lovely amounts of extra poke.
Rageblade is something that I just love to build due to the effects it provides: A good amount of AS, more On-Hit damage, and a passive that doubles all On-Hit effects. This item is by itself a really strong item for Kayle.
Together these items give your build the extreme opportunity of being really versatile. If you build more AP, you gain more dmg to Nashor's passive and if you build more crit or On-Hit items, you increase the value that Rageblade provides.

In short, this build is meant to be a really versatile and reactive build to balance out the game.

So... the core items as discussed before are Nashor, Berserkers, Riftmaker, and Rageblade. This leaves you with 2 item slots. The 2 remaining items are meant to be your reactive and adaptive items. To know what to build is all up to your ability to look at the situation of your game and try to balance it.
What you want to build as your last 2 items are items that provide offense, sustain, or utility. These items can basically be any item that the game provides, there are no wrong items if you know what is the best for the game at that point. Mainly you want your last 2 items to provide at least 3 different things: AP, Crit, or On-Hit effects. It doesn't matter exactly but those 3 variables are what your core items synergize with. AP is to increase Nashor's damage whereas Crit and On-Hit items are to increase your Rageblade damage. I can't fully explain what items you want in which situations, that is something you have to decide on by yourself. On the other hand, I can tell you when should you play or not play Hybrid/On-Hit Kayle.

If I haven't made it clear as of yet, you build like this to balance out the game. Kayle is a fighter-support after all and this is you doing the supporting without being actual support. The decision to play Hybrid happens in champ select. The most common reason to play Hybrid/On-Hit Kayle is when building full AP or AD is not encouraged.
First, we need to know why would you build full AP or AD on Kayle. Kayle is herself a hybrid champion meaning all she does, scales from both AP and AD, so building either one is viable. AP Kayle is most popular for her burst capabilities. Her ult deals the same amount of damage as other mages with big dmg ults. AD Kayle on the other hand focuses on shredding single-target enemies like tanks. Building Hybrid/On-Hit gives these both but at a reduced value. That is not the point of this build though. While you can deal damage, your importance comes with build versatility.

Let's imagine a game where in your team there are Kayle, Rengar, Zed, Samira, and Nautilus. As you can see, your's is quite an AD-heavy team so you'd like to build AP to balance your team out. But in the enemy team, there are Ornn, Rammus, Fizz, Jhin, and Leona. A tank-heavy team, which building AD would be best for. This is the time to go Hybrid. Against tanks, you typically want to build AD items like bork due to the 8% hp passive, but tanks being tanks, they most likely will build armor against your team. This is when you use your versatility to your advantage. The 2 reflex items are AP, now the enemy doesn't have much against you and it's like you would've built AP in the first place. But imagine if they didn't build armor, like in a case where you'd be fed and the rest of your team would be lacking behind, now the enemy has decided on building MR cause you deal mostly magic damage. This is when you pull out the UNO reverse card and keep on building AD, Crit, and On-Hit items. This will lead to them having to give up on the MR and switch to armor, but selling items to change your build is never a good idea. With this build, you don't have to adapt to the enemy team by selling your items and building differently since your core build allows you to go in any direction and still profit.

Another example if you may on when to go hybrid:
Your team has Kayle, Rammus, Veigar, Jinx, and Taric.
Now your team has a good amount of sustain but damage-wise you're a bit short on it. Sure you have 2 greatly scaling damage champions but on a condition that they have to get ahead. Imagine if Veigar gets ahead but Jinx doesn't, then the enemy would build MR. Now it's your turn to balance things out and go AD.

Moments, when you don't want to build Hybrid/On-Hit Kayle, is when going either full AP or AD is more viable. Hybrid Kayle is meant to be a situational playstyle but a capitalizing one. There are many guides on how to play or build full AP or AD Kayle but this guide is on how to be versatile and how to use it as an advantage on Kayle.

Now some of you might think that Hybrid/On-Hit Kayle sounds awesome and broken beyond oblivion. Don't think like this, please. This playstyle is meant to be situational, not something you build every game. This playstyle also requires you to make decisions based on your game knowledge.

Others of yall might think that this build is utter garbage; it lacks damage and sustain. To that I can agree slightly, the build is not meant to carry games, more like be the 2nd best one in your team, since you capitalize on the opportunities that you're given. If you still think that this is not enough, go play some juggernauts. There's enough sustain and damage for you.

Either way, keep this build in your mind and start looking for games where building Hybrid/On-Hit Kayle has its opportunity to shine and win games!