A system for and method of supplying an injection fluid to a well assembly so that the injection fluid flows at a substantially constant flow rate. The fluid can be injected at a single site in the well assembly or multiple sites. A flow control regulator is included that attaches to the well assembly and provides a self adjusting flow control for the fluid being injected. The regulator includes a slidable floating sleeve having an orifice through which the fluid flows. The sleeve includes an inlet port that can register with a fluid supply port to allow the injection fluid to make its way into the sleeve. The fluid exits the sleeve through the orifice to generate a pressure differential across the orifice that in turn exerts a sliding force onto the sleeve. Moving the sleeve misaligns the inlet port and fluid supply port thereby throttling flow through the regulator to a predetermined flow rate.