How do I transfer a single app with data from one iPhone to another?
The best practice in storing app credentials is the Keychain. If you really need to recover the password check out this guide http://www.iphonehacks.com/2013/08/transfer-passwords-to-new-iphone-itunes-backup.html


  In iTunes, go to the “Summary” section, scroll to Backups, and enable
  the “Encrypt iPhone backup” option.


After recovery, feel free to wipe the new iPhone.

In case the app did not store in Keychain, you can use this technique to migrate app data individually http://lifehacker.com/5891964/can-i-transfer-app-data-and-game-saves-from-my-iphone-to-a-new-ipad

Before we start, we should note this works for any iOS device. So if you want to back up and transfer data for iPads, iPhones, or between the two, this works. To manually backup and transfer data, we're going to use the free Mac and Windows program iExplorer. You don't need to jailbreak your iPhone to use iExplorer and it's easy to pull data from your iPhone to transfer it to your new device. Here's how to do it.


Download the app you want to transfer data to on your new iPad.
Plug your iPhone into your computer.
Start up iExplorer and wait for your device to show up in the file
browser.
Click the arrow next to your device name.
Click the arrow next to Apps.
Find the app you want to transfer data from and click the arrow.
Inside the app's main folder is a folder called Documents. That's
where your saved data and game saves are located. Copy it to your
desktop.
Disconnect your iPhone from your computer and plug in your iPad.
In iExplorer, find the app you want to transfer data to on your iPad
using the same steps from above.
Locate the Documents folder and copy all the data you just copied
 to your desktop folder onto the iPad.


That's it, you're done. Different apps use different save files and occasionally the above process will require you to copy several files over. Other times you only have one file. This process works for most apps, but not all of them. Let's take a look at a few of the instances where data doesn't transfer over properly.

Don't forget to look at the caveats because sometimes this technique does not work.