As the field of soft robotics matures, we find an increasing need for improved energy sources. Untethered soft robots have primarily used batteries for electric power and micropumps or cannisters of compressed gas for pneumatic energy. Hydrocarbons present an energy dense and power dense option, but untethered centimeter-scale cyclic soft combustion, similar in concept to an internal combustion engine, is not yet available. As a step toward untethered soft microengines, we present a soft Microfluidic Air-intake and eXhaust (MAX) valve to regulate gas flow in future untethered soft robots. We present a valve and explore the design rules behind key geometry which governs gas flow rates, pressures, and the blocking of flow. The MAX valve is designed to 1. regulate the flow of air into a combustion chamber, 2. regulate exhaust flow from the chamber, and 3. block flow during combustion.