The HTML Flash Viewer is - as the name implies - a viewer only. It is not possible to edit the displayed graph in any way - and that includes opening or closing folders and/or groups. (You cannot do so either when exporting to any of the other supported export formats such as JPEG, PDF, or SVG.)
The first link references a sample application created with yFiles for Silverlight, which is a programming library for Microsoft Silverlight platform.
The second link describes how to program with yFiles for Java, which is a programming library for the Java programming language.
Aside from Java and Silverlight, the yFiles diagramming library is also available for Microsoft .NET (WPF or Windows Form), ActionScript/FLEX, and HTML5.
All of the above are commercial products for software developers interested in creating their own diagramming applications. Please contact yWorks GmbH for additional information.