Kayle & Kayn Synergy
Kayle Top and Kayn Jungle win 53.6% of 2,454 Low Elo games together, +1.5 points vs expected, 2-patch window 26.19-26.20.
Researched on LoL patch 26.20. Tips are written to hold at any rank; stats come from Low Elo ranked games up to patch 26.20.
Playing the duo
Kayle's Divine Judgment(R) can protect Kayn during a dive, but its invulnerability may be wasted if it overlaps the time he spends inside Umbral Trespass(R).
Kayle's Celestial Blessing(W) heals and speeds up a nearby ally, which can help Kayn continue or exit a commit.
How to play as Kayle
Coordinate Divine Judgment(R) with Kayn's commit so the invulnerability covers his approach or exit; avoid casting it just before he disappears into Umbral Trespass(R).
How to play as Kayn
Call your dive before committing and leave Kayle's Divine Judgment(R) for the moment you are targetable; its overlap with Umbral Trespass(R) can waste much of the protection.
Avoid forcing a 2v2 around Kayle before level 6 unless the play is clearly favorable; her early range and ability to protect a dive are limited.
Sources
These notes come from r/Kaylemains, checked against the champions' abilities.