DR doesn't work here at all, since DR doesn't apply to environmental damage. The Boots of the Cat are fine, though, and will still cap your damage to 20 and let you land on your feet.
However, you may also have some confusion about how precisely DR or falling damage works. As a refresher, falling damage is defined with this key sentence:
Creatures that fall take 1d6 points of damage per 10 feet fallen, to a maximum of 20d6.
I'll attempt to clarify what you might be getting confused about.
- You take 20d6 damage if you fall 200 feet, once, not 1d6 damage 20 times.
- Damage reduction applies to the final damage amount, not each individual damage die. (But damage reduction won't apply to the falling damage anyway.)
You take fall damage all at once, when you finally hit the ground. 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. Someone with 1hp will survive the entire fall, so long as they have some kind of strategy for not hitting the ground too hard when they finally reach it.
If damage reduction worked with falling damage, and you fell 200 feet: Boots of the Cat would reduce that to only 20 fall damage, and Shoanti War Paint's DR 1/— would reduce that to 19 fall damage.
If you want to take no fall damage at all, maybe you'd prefer a Wand of Feather Fall, or a Ring of Feather Falling.