Unfortunately, yes. Flat feet leave you with less foot strength and flexibility. The arch of your foot is home to a lot of muscles and is the powerhouse of springing yourself forward for the next stride. People with flat feet are at high risk for overpronation, which is not only painful but also encourages you to put a lot more stress on your knees and ankles, which also slows you down.
However, with the help of motion control shoes, enough cushion and support, and exercises, such as toe curls, you can rebuild strength and increase your running speed.