Unfortunately, App Service on Azure Stack has no support for Windows Authentication and it won't have it since we are consistent with App Service on Azure.
The option is to use ADFS and change the app to authenticate against ADFS.
If you don't want to change the app a lot, you can try using EasyAuth feature of App Service:
https://docs.microsoft.com/en-us/azure/app-service/app-service-authentication-overview