Hi Mark -
Once you have a layer from the local service, you can use the ServiceInfo property of the layer to get details about the service.
The following example creates a dynamic map service layer using the URL of the local service. It then reads the service info and loops thru all layers in the service to find layer ID and name.
Dim localService As LocalFeatureService = Await LocalFeatureService.StartAsync(mpkPath)
Dim dynLayer As ArcGISDynamicMapServiceLayer = New ArcGISDynamicMapServiceLayer(New Uri(localService.UrlMapService))
Await dynLayer.InitializeAsync()
Dim serviceInfo As MapServiceInfo = dynLayer.ServiceInfo
Dim layerInfo As IReadOnlyCollection(Of LayerServiceInfo) = serviceInfo.Layers
For Each info As LayerServiceInfo In layerInfo
Dim id As Integer = info.ID
Dim name As String = info.Name
Next
You could do the same thing with ServiceFeatureTable (sfTable variable in your example) - initialize a service feature table with the first table in the package, then read the service info to determine what else is available.
Hope that helps, Thad