How can I construct a Flowchart in Java Swing?

There are some toolkits that might help with the graph construction. Tom Sawyer's in particular, has some very nice automated graph layout support.

• http://www.jhotdraw.org/
• http://www.tomsawyer.com/
• http://www.instantiations.com/go/

You may also want to perform a web search on "Graph Drawing".