I use Five Ten's with the standard Stealth Rubber Sole, like this:
What does PB recommend for best flat pedals that stick to this shoe? I'm running some Specialized flat pedals (the aluminum ones that come with the Demo) but I was wondering if there's anything better out there.
Five Ten's are among, if not the best shoes for flat pedals. Not the other way around. Choose your pedals based on your criteria: size, thickness, material, shape, weight, color, price etc.