[ericscheid]

Consider this code to duplicate a selected graphic

tell application "OmniGraffle Professional 5"
	set theSelection to the selection of front window
	set theObject to item 1 of theSelection
	duplicate theObject
end tell

How do I get a reference to the new graphic?

You can duplicate it to a particular position in the graphics collection, and then reference the graphic at that position:

tell application id "OGfl"
	tell front window
		set theObject to item 1 of (selection as list)
		tell its canvas
			duplicate theObject to end of graphics
			set oDuplicate to item -1 of graphics
		end tell
	end tell
end tell