Inflatable robots are becoming increasingly popular, especially in applications where safe interactions are a priority. However, designing multifunctional robots that can operate with a single pressure input is challenging. A potential solution is to couple inflatables with passive valves that can harness the flow characteristics to create functionality. In this study, simple, easy to fabricate, lightweight, and inexpensive mechanical valves are presented that harness viscous flow and snapping arch principles. The mechanical valves can be fully integrated on-board, enabling the control of the incoming airflow to realize multifunctional robots that operate with a single pressure input, with no need for electronic components, cables, or wires. By means of three robotic demos and guided by a numerical model, the capabilities of the valves are demonstrated and optimal input profiles are identified to achieve prescribed functionalities. The study enriches the array of available mechanical valves for inflatable robots and enables new strategies to realize multifunctional robots with on-board flow control.