[dannythefool]

Not really sure what you're doing; single objects flip for me with the flip button in the "Properties: Geometry" inspector pane. However, only the shape itself is flipped, not the content. So flipping a rotated box filled with a gradient that also contains text still won't do anything, for example.

If that's your problem, here's a workaround: Select object, right-click, Copy as -> PDF, and then paste that. The pasted vector graphic can then be flipped, including all text. Note that you'll still be able to edit it in OmniGraffle, just double click the vector graphic, edit in the new window, and save.