Using urban planter boxes on a fire escape is a common desire for city gardeners seeking green space. However, the primary answer is that it is generally not allowed and is often unsafe. Fire escapes are designated as emergency exit routes, and local fire and building codes strictly prohibit obstructing them with any objects, including plants. Adding weight and creating tripping hazards can prevent safe escape during an emergency, risking lives and potentially resulting in fines.
Before considering any gardening on a fire escape, you must check your local municipal fire codes and your lease or building rules. Most explicitly forbid it. For a safer alternative, explore indoor container gardening, window boxes installed securely on the interior side of the ledge, or community garden plots. If your building has a proper, structurally-sound balcony intended for use, that is a far safer location for planter boxes. Always prioritize safety and legality over gardening ambitions in shared escape pathways.