Sunny, I think he means poles as in weaving in and out. The best way is to teach him the pattern slowly so that he knows what you want before asking for any type of speed. Having him run too soon will only confuse him and you may end up with behavior problems.
Any horse can be taught to run poles - only a few will be good enough to compete and Walking horses are not known to be as competitive as other breeds.
Walking horses (or at least most that I know, includeing Sunny) are GREAT at weaving poles. Sunny LOVES to turn fast! And Magic, anther Walker I know, is extremely good at them.
So breed-wise, you're probably set!
Like Iridehorses said, working slowly and working your way up is the best way to train them to it. Although that can be a bit challenging on a gaited horses as they have so many "slow gaits" and "fast gaits" and "in-between gaits", try to stay as close as you can to a flat walk, and then to a rack, and then eventually to a canter. Don't let him drift around through gaits. Keep him collected and in your hand, but give a bit when you turn the corners. Give him your leg if he drifts slower.
And when you say "trot" you do mean gait, right? By your username I automatically thought "gaited horse", lol