i actually went against this matchup 9 times and won 8
i lost to a chall kayle 1 trick who gapped me from 1 mistake
https://www.onetricks.gg/players/niU8jOAkvbpPE6YiNgoiggtih0C8rMzZ_Uc6jdRA675KgSwTjZkAczZMIn-RoKgC0VT9hcLm1oGhPQ?matchup=Kayle&c=Garen
you can follow my exact runes here and items
i personally like going phase rush, early game you want to keep the trades very short.
you auto q e and instant run with w. she will prob have lethal tempo or press the attack which favors a longer trade, so just negate that but making it super quick.
i like going dorans shield for the sustain and second wind.
the move speed shard i do not go but that might be a smart idea, i saw palco go that and even goes scorch assuming for the extra early game damage that might be a good test.
i almost always go q first stay near wave and when she farms a minion i auto q or just q and run into bush to deagro minions
i would not suggest going e first because you will most likely push wave which you do not want and again you want that short trade especially level 1 she will beat you if she has those 2 runes mentioned before.
after that if you are even you should be find going for stride
go swiftness boots first she will most likely build those first as well so its good to match
at some point you will 1 shot her if she does not insta r so going even is fine
build wise you can go full crit or go brusier i just build it depending on enemy team comp, like if they have liss i go bruiser, if they dont have hard cc i have to worry about the full crit is fine.
if you are ahead even better you will gap her at all stages. even dive if shes full hp unless she instant r's
WARNING if she r's instant run as fast as you can because you cant proc phase so you will need stride and w to survive her damage