How do I flip a photo horizontally or vertically in iPhoto?

You will have to use another application. Preview will do it. Set up iPHoto to use Preview as the editor of choice. Then double click on the thumbnail to open it in Preview, flip the image and save.

Using 2 Image Editors in iPhoto
If you want to use both iPhoto's editing mode and a 3rd party editor without having to go back and forth to the Preference pane, once you've selected the 3rd party editor as your editor of choice, reset the Preferences back to "Open in main window". Then when you Control-click on an image, you can select "Edit in external editor" in the Contextual menu to edit in your selected editor.