It is a judgement call by the ump on which it hit first. It would be a dead ball either way. If it hits the finger first, the ball is immediately ruled dead and a strike is issued. It doesn't matter what the ball does after that (hit the bat, go into fair territory, pop up that is caught, etc). This is a strikeout if there were already two strikes. If it hits the bat and then the finger, it is just like any other batted ball that hits the batter. If he was still in the box and it was unintentional, it is immediately called a dead foul ball. This is not a strikeout if there were already two strikes, unless it was during a bunt attempt.