I am not knowledgeable about the problems associated with flat feet, but it does not seem that the condition itself would affect your ability to move quickly.
Different people have different natural talents for movement. As you see on the dance floor, some people naturally relaxed and move gracefully while others move stiffly and awkwardly. If you watch professional boxers, some dance around effortlessly while others prod around stiffly. Some people move smoothly and attack quickly, while others move more slowly and attack with power. Both methods have their pros and cons; however, would you rather be hit with a quick punch from a dancing Sugar Ray Leonard or with a power punch from a prodding Mike Tyson.
To get better at performing a side kick, you specifically practice the side kick repeatedly for months. To get better at moving, you must specifically practice moving. Jog on rocky, uneven trials, jump rope, or shadow box to your favorite upbeat music. When practicing punches and kicks on a workout bag, concentrate on improving your foot movements. Build your leg muscles using squats and plyometric jumping exercises.