You have a few options if you’re looking to copy Azure app settings and connection strings between Azure Web Apps. One of those options is using the Azure portal, copy and pasting until the task is completed.
Alternatively, you could use a tool to help automate the process. One such tool is the Azure Web App Configuration Copier — which was created to fill a potential need by the Ritter Insurance Marketing development team.
For usage instructions, see the README.md in the ritterim/azure-web-app-configuration-copier GitHub repository.
For more information, see this post on the RIMdev blog.