If you purchased it, then chances are it's not one "sold" by the church as all church apps are free. You'll have to check with the vendor on their licensing.
But if it's the church app, I think it would be easier to get it from the market then to try to exact it from the Kindle.
Have you searched the Wiki
Try using a Google search by adding "site:tech.lds.org/wiki" to the search criteria.