Final answer:
The most likely diagnosis is Superior vena cava syndrome.
Step-by-step explanation:
The most likely diagnosis for a 64-year-old man with a headache, cough, facial edema, facial plethora, prominent venous distention of the chest, and a history of lung cancer is Superior vena cava syndrome. Superior vena cava syndrome occurs when there is obstruction of blood flow through the superior vena cava, usually due to a tumor. In this case, the lung cancer is causing compression of the superior vena cava, leading to the symptoms described.