We're terribly sorry you experienced this. Can you give us some more details about your iOS 10 upgrade, like:
Did you update over the air? Did you have little free space on your phone when you upgraded?
Did you get this dialog during upgrade? http://wpuploads.appadvice.com/wp-content/uploads/2015/06/appdeleted.jpg
If you sync via iCloud, it's possible that icloud still has your speed dials. You can try to delete the app and reinstall it. Other than that I don't have any good advice, since app data is unavailable to normal users, there are no easy solutions...
Best of luck!