The change style option is non existent for feature layers I've created by using the copy command in a web map. This seems to occur for hosted feature services and arc server services. Adding the data using the add button will bring in a 'layer' that can have the style changed. I'm curious if this is a bug or by design. It was much more convenient to duplicate single layers rather than bring in entire services.
I believe this issue was introduced after the latest update to ArcGIS Online. It may be worth following up with Tech Support in regards to this. If this is a bug, they will log it so that development is aware of the issue.
