As amaitland said, this is not supported.
To use proxies with CefSharp you can use this code, but the Initialize method can only be called once per application domain.
CefSettings settings = new CefSettings();
if (string.IsNullOrEmpty(proxyAddress) == false)
{
settings.CefCommandLineArgs.Add("proxy-server", proxyAddress);
}
//validate if the CEF instance was already initialized
if (Cef.IsInitialized == false)
Cef.Initialize(settings, true, true);
chromeBrowser = new ChromiumWebBrowser(url);
a workaround could be to use each WebBrowser instance on a different application and call it as a new process.
Hope this help