You want to prefix your service url with the proxy url.For example:
var str = "http://serverapps.esri.com/SilverlightDemos/ProxyPage/proxy.ashx?http://sampleserver3.arcgisonline.com/ArcGIS/rest/services/HomelandSecurity/operations/FeatureServer/2?f=pjson";
WebClient w = new WebClient();
w.DownloadStringCompleted+= (s, e) =>
{
};
w.DownloadStringAsync(new Uri(str, UriKind.Absolute));