How come that person is so much faster at kicking than I am, I hear you say, you always kick hard but for some reason you are not that fast.
Lets take a look at some things you can do when you are practising that will help.
Improving your flexibility in the ankles is the first starting point, I have always found that this is difficult to ask a swimmer to regularly do. Us humans need something to trigger us to remember to do it, especially if you don't have access to daily coaching sessions with a coach that gets you to do it regularly. So we need something to remind us / nag us - so think of a regular thing you do twice a day that will prompt you and only lasts a few minutes. The one I always advise is stand on you toes when you are cleaning you teeth. It sounds mad but you do it twice a day, it lasts only a short while, its easy then to remember and its not easy. Try it - don't hold on though
Next lets work on exercising the right muscles - they way I like to do this is slowly, so put some fins on and kick on you side with a very wide straight legged kick, its important to do it wide, keep the legs straight and slowly so you are encouraged to feel the resistance throughout the kick. I have been doing this for quite some time with swimmers now and you regularly see a swimmer kick backwards far, but with one or both legs not kick very far forward very far. This is an indication that they have a weakness in one of there muscles which when you kick fast never gets corrected. So slow wide kicks on the side with fins on, try it - its not easy.
Give that a try and let me know how you get on, more on kicking to follow