You say you're building a one page site, so that could change a lot about how your views are arranged and served to the user, but in general, you'd have a Story controller for each story where you want to display the slides. In that controller, get the Slide children of the current TreeNode, then feed those into a ViewModel for the Story view.
var slideNodes = DocumentHelper.GetDocuments<CMS.DocumentEngine.Types.MyNamespace.Slide>().Path(currentNode.NodeAliasPath, PathTypeEnum.Children).OrderBy("NodeLevel ASC, NodeOrder ASC");
You could feed them directly into the ViewModel for the Story controller from there, or best practice would be to create another ViewModel for the individual slides.
storyViewModel.slides = slideNodes.Select(n => new MySlideViewModel() { Title = n.Title, Image = n.Image });
Also best practice would be to use the DocumentQueryService rather than the DocumentHelper directly, as well as the CacheService to lighten the load for future requests. Hope that points you in the right direction!