FeatureLayer needs a service to work against, so the only thing you can really clone is Url, but that means your features etc are also pulled from the service there, and that's probably not what you want.
Instead create an empty GraphicsLayer and use that to edit instead (you could copy the Renderer over to get some similar rendering). However, then TemplatePicker might now work that well, and you might have to go a little bit more low-level and the Draw class instead. The TemplatePicker is really designed to work with a FeatureLayer(s) backed by a FeatureService.