You'll generally want to ride with your feet in the clips. You can damage the clips if you are riding on the flat side because it is possible for them to strike the ground. At best you'll abrade the nylon clips, which isn't a big deal, but at worse, the material will fracture.
I have BMX style platform pedals with fixed pins/spikes similar to those in irclean's image above. I've hit the pavement a few times while making aggressive turns with the inside foot down by accident a few times.
In case you do end up getting those Avenir pedals from Amazon, you might want to remove the screws that hold the clips on and then clean them with degreaser like Simple Green and/or denatured alcohol and then apply a bit of thread lock before put them back on. Maybe it's just my bad luck, but I've had two sets of similar pedals where the screws came out within the first 15 miles, or so, of riding.