Which method of fire extinguishing involves using foam or dry powder?

The method of fire extinguishing that involves using foam or dry powder is smothering. This approach works by covering the burning material with a blanket of foam or dry powder, thereby eliminating the oxygen that fuel needs to continue burning. Foam can in particular expand on contact with the fire, creating a barrier that prevents oxygen from reaching the flames, while dry powder agents effectively interrupt the chemical reaction that sustains the fire.

In contrast, cooling involves applying water to lower the temperature of the burning material, which can be effective for certain types of fires but is not specific to using foam or dry powder. Starvation refers to removing the fuel source from the area of the fire, which is a different approach altogether. Flushing generally refers to using water or another liquid to wash away flammable materials, which does not directly relate to the principle of using foam or dry powder for extinguishing fires. Thus, smothering is the correct answer due to its specific focus on suffocating the flames using these fire suppression agents.