Do you have a little more background on the horse? Is this a young horse that is figuring things out, or an old horse that has just learned to respond to the person on the ground and ignore the rider?
Teaching any cue has to do with timing, consistency, and release. With my young ones, I usually start from the ground. I always use the same cue for walk, same cue for trot, and same cue for canter. That goes for physical and vocal cues. When you are doing ground work, imagine your line as your rein aid and your whip as your leg aid. It is very important that you are behind the horses drive line. Start with a vocal command, then follow through with using the whip lightly. I start with tapping right where the leg would be, and for a horse really lacking forward, I will move to the hind end. Increase pressure gradually and continue rhythmically with the whip until he makes the slightest effort forward, and then release all pressure and praise. Every time you do this, he will respond sooner and sooner and if you are consistent, he will begin to respond to the voice. Start expecting more as far as how long he maintains his walk and what kind of effort he puts into his walk.
When you transfer this to the rider position, use the same vocal cue, the same timing between vocal and leg (immediate, less than 3 seconds), and carry a crop at first for the same reinforcement if he does not respond to the leg.