I was just reading about wind resistance and tire rolling resistance a few days ago. The conclusion was, at less than 10mph and less, the tire's rolling resistance matters. When riding at speeds above 10mph, rolling resistance is no longer an issue as it is the wind resistance that is the biggest thing slowing you down. That tells me that the only way to sustain a faster speed above 10mph, is to have stronger legs and to find a way to be more aero on a flat bar bike. Both of those have already been suggested by previous posters. Maybe switch your tires to 32mm Schwable G-One speed and slam your stem so you can get lower and more aero.