In most cities, the short answer is no: urban planter boxes are generally not allowed on fire escapes. Fire escapes are regulated as emergency evacuation routes, so they must stay clear of storage, furniture, grills, and other obstructions. A planter box can block movement, create a tripping hazard, add combustible material, and become a falling object during a fire or high winds. Even lightweight or decorative planters are usually treated as obstructions.
Some cities may have local rules that vary, and a few older buildings may have specific allowances, but the safe assumption is that fire escapes must remain completely unobstructed. If you want to grow plants, use ground-level planters, approved window-sill planters, or a balcony garden where local codes and building rules allow it. Before installing anything, check your city's fire code and building management rules. Violations can lead to fines, forced removal, and liability if an emergency occurs. In practice, most cities prioritize life safety over decorative planting, so keep fire escapes empty and use safer alternatives for urban gardening.