I was using WebPageTest to test the performance of my Azure Web App (ASP.Net vNext Web API/Angular). I got an F for both \"Compress Transfer\" and \"Cache Static Content\".<
gzip compression is enabled by default for Azure Web Apps. You can see the rules in your sites LocalSiteRoot/Config/applicationhost.config. Looking at the response headers (which can easily be done with developer tools) should confirm that gzip is being used. It is possible that one of the resources that your site loads is not compressed, and this is causing the WebPageTest to fail. I would look at a network capture and the response headers, and see if you can find the offending resources if you're concerned.
To go to the local site root, you can use FTP, or go to your SCM site at https://.scm.azurewebsites.net/DebugConsole and then click the globe icon.
Also I suspect that your 2 javascript files are not getting compressed since the Content-Type header is not getting populated, so the rule is not capturing it because it does not recognize the mimetype.