@Meddler, while the team is looking at fixes for kayn's interaction with items/proc
Since it has been confirmed that assassin's kayn's passive not interacting with items is something that is a bug that needs to be rectified there is other item/proc interactions (some not 100% confirmed) that need looking at.
From testing it has been confirmed that corrupting potion is the go to for lane kayn to increase his stack rate for his pre-transformation passive. It has been tested and confirmed that DFT has a similar interaction of increasing stack rate. Other items that have been tested and confirmed to give more orb stacks is tiamat and their hydra upgrades, protobelt (yes I know obviously not a good choice but it is no joke that everything was tested), thornmail drops one every hit, chilling smite drops 1, and challenging smite drops multiple for the dot. One item that could be an option for the darkin mode but has zero interaction to the point that I think it should be grouped as a a bugged item interaction is bami's/cinderhulk.