[JKT]

Copy the object as a PDF. Paste it as a PDF. Scale that newly pasted PDF object and the lines and text will scale with it.

Because OmniGraffle uses LinkBack, if you need to edit the PDF object (e.g. you decide you want a different fill), just double click it and the PDF will open a new LinkBack window with the original editable object displayed. Perform your edits in that window and when you save the LinkBack window, the edits appear in the object in the original document.

You can watch a short demo movie (~3MB in size) of how this works here which is probably a bit easier to follow than the description above ;)