Thank you @abra.
I was able to find a work around for this issue.
By using the KeyEvent argument of the dispatchKeyEvent() method from the KeyEventDispatcher interface I was able to determine the associated KeyStroke used to generate the KeyEvent. This enabled me to find the JMenuItem (if any) in the application's main JFrame with an associated KeyStroke accelerator. Once I have the JMenuItem associated with the KeyStroke, it can be programmatically activated by the JManuItem doClick() method.
This efictively redispatched the KeyEvent from the child JDialog to the application's main JFrame.
I suppose KeyBindings could have solved this issue but as this is legacy code, reworking the Menu structure of the application main JFrame would have been a less optimal solution.