Microfluidic paper-based analytical devices (μPADs) are a versatile and inexpensive point-of-care (POC) technology, but their widespread adoption has been limited by slow flow rates and the inability to carry out complex in field analytical measurements. In the present work, we investigate multilayer μPADs as a means to generate enhanced flow rates within self-pumping paper devices. Through optical and electrochemical measurements, the fluid dynamics are investigated and compared to established flow theories within μPADs. We demonstrate a ∼145-fold increase in flow rate (velocity = 1.56 cm s-1, volumetric flow rate = 1.65 mL min-1, over 5.5 cm) through precise control of the channel height in a 2 layer paper device, as compared to archetypical 1 layer μPAD designs. These design considerations are then applied to a self-pumping sequential injection device format, known as a three-dimensional paper network (3DPN). These 3DPN devices are characterized through flow injection analysis of a ferrocene complex and anodic stripping detection of cadmium, exhibiting a 5× enhancement in signal compared to stationary measurements.