Does Detonation Amplifier killing a unit as the cost of a Deathknell unit trigger it twice?

Yes — as long as the unit you kill is a friendly unit at Detonation Amplifier's battlefield, its Deathknell is added to the chain twice and both copies resolve.

Amplifier's last line is a static ability, so it doesn't matter why the unit died — a kill as a cost, a spell, or combat damage all count. What matters is that Amplifier is already in play when the trigger is created, and it is: permanents enter play and only then get their "when you play this" trigger put on the chain, so the "trigger an additional time" static is live while you're paying the kill. The kill in "you may kill another friendly unit or gear to draw 1" is a cost within instructions, so it's paid while that play trigger is finalizing (Rule 383.3.b) — the Deathknell just sits on the chain and resolves after the draw.

Two caveats: the dying unit must be at Amplifier's location ("here") and must be yours, and if the death is replaced (e.g. Zhonya's Hourglass), there's no Deathknell trigger at all, let alone two.