Depending on what material the scissor jack is made of, it might be difficult or tedious (or both!) to drill all the way through it. If so, another idea might be to only drill through the chuck until you hit the jack, thread the drilled hole to take a bolt, and tighten the bolt to press against the scissor jack thread. It wouldnt 100% guarantee the jack from turning independantly but it would give maybe 80-90% resistance, which hopefully would mean that unless the jack got jammed and the drill still tried to turn, it should be effective to keep the drill and jack rotating together.