If the app doesn't show up there, you'll need to contact Apple's iTunes support team to see if there's anything they can do. Then to check the purchase history for that Apple ID, you'll need to use the desktop version of iTunes - detailed instructions and screenshots are available here from Apple.
To do this, go to the main Settings menu (silver gear icon on Home screen) > iTunes & App Store > Apple ID. First, you'll need to check which Apple ID is being used on the device. If the app is not showing up as 'Purchased' on the device, you can check the purchase history in iTunes to make sure the app was purchased on that ID. Once you've found the app, tap the cloud icon next to the name to download and install it. In this view, it's possible to sort by app name (check the top right of the screen for a dropdown) or search (at the top left), which can make it easier if you are using an account with many apps. Tap 'Purchased' in the bottom navigation bar.Find the version of Kiosk Pro you purchased previously and tap the download icon to install.Select 'Not on This iPad' at the top of the screen.
If you have deleted an app, you can redownload it for free using the same iTunes account that you used to purchase it originally: Can I redownload an app I have purchased?