Here is a link to my vibrating lap. It works on an off centre cam shaft which causes the tray to vibrate. The final polish, as in the video is done with dry tin oxide on a nylon carpet. I have found with experimenting that dry tin oxide gives a better and faster polish than using it as a thin, wet slurry.
The following is a gallery of agate samples from various localities in New Zealand. The specimens have all been flat lap polished. Click on the thumbnail to see the full picture.