A flame arrester functions by absorbing the heat from a flame front traveling at sub-sonic velocities, thus dropping the burning gas/air mixture below its auto-ignition temperature.
Consequently, the flame cannot survive. The heat is absorbed through channels (passages) designed into an element.
These channels are chosen and measured as the MESG (maximum experimental safe gap) of the gas for a particular installation.
The required size of the channels needed to stop the flame front can vary significantly, depending on the flammability of the fuel mixture.