Using Facebook to promote your contest is also going to result in more comments, more likes and more views. What this means is that more people are going to know about the contest, even the ones who are not following you on Instagram.
If they want to take part in the contest, they will then follow your business on Instagram, meaning you are going to gain new followers. Plus you are going to use the visibility of Facebook to continually increase the number of participants that are going to send in photos for the contest that you are hosting.