So far, there was a limitation on the Web Deploy feature where the proxy was not supported.
If you try to publish using Web Deploy to Azure Web Sites over Proxy, then you would run into error something like:
"Could not connect to the remote computer ("****.scm.azurewebsites.net"). On the remote computer, make sure that Web Deploy is installed and that the required process ("Web Management Service") is started. Learn more at: http://go.microsoft.com/fwlink/?LinkId=221672#ERROR_DESTINATION_NOT_REACHABLE"
You might get the above error for many reasons while deploying to Azure Web Sites and one of the reasons is if you are trying to use proxy.
With the latest version of the Web Deploy 3.6 (BETA), the proxy support has been newly featured which helps you to address the above error.
Add the below code snippet to the msdeploy.exe.config file after the installation of the latest Web Deploy 3.6
<defaultProxy useDefaultCredentials="true" />