If I have a Reflection copy of Karthus, and a Soaring Scout at a battlefield, and my opponent moves in with enough might to kill both units, does Karthus trigger the Deathknell a second time?

Yes — Soaring Scout's Deathknell triggers twice.

Karthus's ability ("Your [Deathknell] effects trigger an additional time") is a passive ability, not a triggered one. Because it's passive, it doesn't need to "survive" and stays active at the exact moment both units die. When combat damage is dealt simultaneously (Rule 460.2.c.1.a), both the Reflection copy of Karthus and Soaring Scout receive lethal damage at the same time. At that moment, the Reflection Karthus's passive is still applying to the game state, so Soaring Scout's Deathknell trigger is created with the modification — triggering once for its base Deathknell and once additional from Karthus.

The Reflection token copies Karthus's static ability just fine — its built-in restriction only blocks "play effects" (like "When you play me" triggers), not passive abilities like this one (FAQ #11575). You end up with two Deathknell triggers from the Scout.