Attach to a target unit. If attached unit is damaged, destroy that unit.

What happens if I attach Branded by Khorne to a unit that already has some damage on it? Is it destroyed?

Or should I give the unit some damage after BbK is attached to it in order to destroy the unit?

The latter. Branded by Khorne only works with damage dealt after it has been attached.

should read, "when unit becomes damaged…".