Sprint training is done by legspeed exercises. Start at 100rpm cadence and hammer away until you hit your maximal cadence somewhere in the range of 150 to 200rpm depending on how well developed your legspeed is already, then shift in higher gear unless you run out of power.
But since you have a fixed gear, roll down a hill where you can hit 100-110rpm cadence and start sprinting at full force. Make it count like you want to rip the crank of your bike. Do that about once a week.
Need to build up your fast twitch muscles. I do interval training about one out of four hours riding. I'd find that hard to do on a fixed gear, but YMMV. Weight lifting also helps. Things like squats, step ups, lunges, leg extension, calf raises. I tend to do them at lower weight-high rep, but you may want to try them at relatively high weight to pack on the muscle. If you do that you should probably have a spotter. Be careful to build up slowly.