To learn to hit as you move you have to do it. Start by coming toward a standing person with your fist up and touching him without pushing as you continue to move. Do this several times till you can lightly touch without changing your pace. Now walk toward the person with your hands in natural positions (relaxed) and place your hand AS you walk. Advance to pushing and than to hitting. After you can deliver one hit without changing your pace or changing your form (leaning or rotating your torso and legs) try for two hits and see how your body solves this. Once you can do tow advance to doing these drill as the other person walks as well as he wishes and grow from there. Avoid putting too much importance on actually hitting. It will tense you up and you will forget your own safety and what creates it (the four principles) Another way to develop hitting while moving is to have two people exchange hits as they walk together or run together. It is also rather amusing to watch. After a few of these drill try a more open enviroment by having a mass fight. Everyone hitting and pushing and levering each other as they move and position themselves the best they can in the crowd. have fun.