I had Duchess of Albany, Fireworks, Jackmanii Superba and Jackmanii all under the black walnut trees. They did fine except there wasn't enough sun, so the clematis didn't bloom much.
One thing to keep in mind when planting anything under a black walnut tree is that the fully leafed out canopy sheds water. We can get heavy rains, the rest of the garden will be well watered, and many times I still have to water the hosta under the BW trees. Black walnut trees are also very heavy feeders. The feeder roots seek out moisture and nutrients, so if your clematis is near a root, the tree is probably taking the nutrients.