How can I be notified when a Snackbar has dismissed itself?

Google design library supports Snackbar callbacks in version 23. See Snackbar docs and Callback docs.
You will then get notified when the Snackbar gets dismissed (and also when shown) and also the type of dismissal if this is useful for you:

snackbar.addCallback(new Snackbar.Callback() {

    @Override
    public void onDismissed(Snackbar snackbar, int event) {
      //see Snackbar.Callback docs for event details
      ...  
    }

    @Override
    public void onShown(Snackbar snackbar) {
       ...
    }
  });