You can use FeatureLayer to get metadata from the service or you can GetDetails from ArcGISDynamicMapServiceLayer.
var l = new FeatureLayer() { Url = "http://sampleserver3.arcgisonline.com/ArcGIS/rest/services/Fire/Sheep/FeatureServer/0" };
l.Initialized += (sender, eventArgs) =>
{
if (l.LayerInfo != null)
{
var fields = l.LayerInfo.Fields;
}
};
l.Initialize();
var m = new ArcGISDynamicMapServiceLayer() { Url = "http://sampleserver3.arcgisonline.com/ArcGIS/rest/services/Fire/Sheep/MapServer" };
m.GetDetails(0, (layerInfo, exception) =>
{
if (layerInfo != null)
{
var fields = layerInfo.Fields;
}
});