If I star-crossed a reflection unit that has a deathknell effect, does that deathknell effect trigger?

No, the Deathknell effect will not trigger.

According to Rule 808.1.d, the trigger condition for Deathknell is the permanent being killed and sent to the trash.

Star-Crossed instructs you to return a unit to its owner's hand. Because the unit is moved to the hand and not the trash, the condition for the Deathknell ability is never met. Therefore, the ability does not trigger. This is consistent with how other effects that move a unit to a zone other than the trash (such as recalls or banishes) interact with Deathknell (see Rule 808.1.d.1 and RiftJudge FAQ #9664).