I don't shoot while walking much, but I find that whene shooting at fleiting targets from a moving platform you can't rely on sites as much. At least I can't, I keep both eyes open, concentrate on the target, and "feel" where I am aiming. This works best for me. Incase you're wondering my brothers and I let the top down on our Jeep and shoot off it while driving around our ranch. Loads of fun!
Hope this helps,