I agree with Donald that any fly, within reason, can be used on any rod. Tenkara rods really push the envelope with respect to using a light line, though, which is essentially just a very long fly fishing leader. I've only tried to fish a Hewitt Spider once with a tenkara rod. It was so wind resistant that it was hard to cast. Imagine trying to cast one with your fly rod, with a 15' leader and no fly line past the rod tip. I think a very wind resistant fly, like a Hewitt Spider, or a very heavy fly, like a double bunny, are no longer within reason for a tenkara rod.
Most tenkara style flies are wet flies. The forward sweeping hackle, which in Japan is NOT at all sparse, almost acts like a sea anchor, providing some resistance and pulsing when the line is tightened to work the fly.