Damage reduction reduces the damage from the total, not the individual dice. From the D20 Pathfinder SRD's section on Falling Damage (emphasis added):
Creatures that fall take 1d6 points of damage per 10 feet fallen, to a maximum of 20d6. Creatures that take lethal damage from a fall land in a prone position.
If a character deliberately jumps instead of merely slipping or falling, the damage is the same but the first 1d6 is nonlethal damage. A DC 15 Acrobatics check allows the character to avoid any damage from the first 10 feet fallen and converts any damage from the second 10 feet to nonlethal damage. Thus, a character who slips from a ledge 30 feet up takes 3d6 damage.
You take 20d6 damage if you fall 200 feet, once, not 1d6 damage 20 times.
If you have any damage reduction capable of reducing fall damage, it reduces the total damage. In your example, let's say you fell 200 feet: Boots of the Cat means you take only 20 fall damage, and Shoanti War Paint's DR 1/— reduces that to 19 fall damage. You still land on your feet thanks to those boots.
If it makes it clearer: you take fall damage when you hit the ground, all at once. You don't progressively take 1d6 fall damage per 10 feet whilst falling through the air. The increasing number of damage dice is not taking damage from the air, but an increasing measure of how hard you're going to hit the ground when you finally reach it.
Maybe you'd prefer a Wand of Feather Fall, or a Ring of Feather Falling?