Manamune into crit has been working for a while and even many streamers have been trying it. It's really strong late game and you can basically melt people. However the AP build is still the meta and people in high elos (master+) prefer that in most situation. The thing about Kayle that many people don't actually understand well is that her passive works twice. 1st when you AA someone and 2nd when the Wave hits them. Meaning that if you E passive says you deal 200ap with each aa, you actually deal 400ap and that's what makes AP build really good. It gives a really good amount of damage in late game.
However, in some match ups and team comps it's better to go for other builds. Kayle can build nearly anything! I've been trying Grasp/Tank kayle in ranked yesterday and it worked pretty well. People kept to All-In me expecting me to die like other Kayles but I ended up killing them instead. I went for so it was easy to kite them. I'm trying new builds for new patch.
New patch is a balance patch. Kayle used to farm with Q early but now if she does that she'll run out of mana easier but her E won't cost mana anymore so it can be pretty good to farm safely until lvl 6. it deals more damage to low hp targets so it's perfect for farming. I personally see it as a buff. I'm gonna max E first and bully people with it xD. Thatt's why I've been looking for runes that can work well with her E. I'll update the guide when I've finished the experiments.

same, but mid and top are better to me. as adc, I get punished early and mid game (and it has the lowest exp alongside with sup). as a jg, I can't help early and its exp is lower than mid and top. (I pick it only if the enemy is tanky and I wanna go onhit.) and I only pick her as sup when playing with a premade.
and the reason I didn't mention roles was because there's a limitation for writing letters on title. I really like putting my favorite quotes of champions on their guide title xD.
thanks for writing on my guide. have a nice day.

I understand. Just because those exist, it doesn't mean you can go for them in any situation. I don't really suggest those unless you're playing with premades. those roles need a lot of experience since Kayle isn't supposed to be there. it doesn't mean those won't work out well. I myself tried them and those can sometimes work out pretty well. but mid and top are always better choices since those roles give a lot of exp and you have a tower to defend you.

Conqueror takes longer than them to get activated and it gives half amount of lifesteal. It's not comparable to other runes. (even if you use both Q and E you still need to Auto Attack your opponent 6 times to get it activated (which you shouldn't. E is finisher). btw, even with melee animation, all your basic attacks after level6 get counted as ranged).
And about Fleet Footwork, It's more of Defensive Item on Kayle. Kayle is a Lategame Hypercarry and These 2 runes don't give her as much benefits as PTA and LT.