This question was posted previously but was marked as "solved" and won't allow me to post on the thread.
The answer indicates this would be implemented before the viewer was brought out of beta, but I'm still not seeing it now that the viewer is out of beta. @ChrisWhitmore - has it been implemented? Thanks!
It looks like you can't, at least not right now. In an app based on the "new" generation of web maps, a layer list will allow you to toggle sub-layers individually.
As far as dynamically re-styling the sub layers for a specific map, you'll need to use the classic map viewer for now.