You can install Sprout on other devices without having to pay for it again as long as the other devices use the same Apple ID. If you have already purchased the app on one device, on the other devices, you can tap the "BUY" button in the top left corner of the app and then tap the "Restore Your Purchase" button. Enter your Apple ID info and then you'll restore your purchase onto this device.
You can also use Apple's Family Sharing feature that became available in iOS8. All devices need to be running iOS8 or higher in order for this to work.