In FPS games stealth takedowns are usually performed when approaching a target from behind (crouching) and pressing the melee key. Enemies have often killed me with a finisher move in Battlefield 1.
How instant stealth kills work? One possibility is to run and hold melee to do a bayonet charge, but that can't be the only way as it wouldn't work in close quarters.
UPDATE: This likely was an issue with the beta, melee finishers now function as expected.