When an iOS app is uninstalled, its settings and data are uninstalled with it.
Sometimes, you'll notice that when you reinstall the app, it will 'remember' some data from the previous install. That's because apps can store info on your device and on their servers.
Some apps store your info on their systems or 3rd party providers and they identify your device that way. Sometimes it's as simple as the email address you provide when you create your account.
Also, Apple allows developers to call their developer framework to get a unique number for each device. That a developer can access and store that number on their servers so they'll know if the same device or account has used their app in the past. The only way around that is to completely wipe your device and set it up as new again.
As each app developer is different, and you don't know what code they implemented, the only way to find out if you can setup the app as brand-new again is to contact the developer or delete the app, restart your device, and reinstall the app again.