The Short Answer:
Wade through the promo material that's loaded into the free version
Click the + Video button at the top to add the video you want to flip
Click the Rotate button below your video
Click "Horizontal Flip" or "Vertical Flip", depending on which way you want to flip your video
Finally, click the Run button to process your video -- the new file will be saved and VideoProc will open the folder where it saved it
The Longer Answer:
There isn't one! If you run into questions or have issues, feel free to post a comment. The one other thing you might want to consider is your preferred output format. I typically use the default MP4 target format.
If you like Video Proc, consider buying it. Last I checked, the one-year license was discounted to about $30. It's one of those tools that does common things simply, without trying to be a full-featured video editor.