The man is looking at a picture of his son.
Careful analysis of the statement, "Brothers and sisters I have none, but this man's father is my father's son", will reveal this to be the case. It is not possible that he could be looking at a picture of himself. The main phrase is, "That man's father is my father's son." Which means: "That man's father is me." (Your "father's son" is yourself if you have no brothers or sisters, as the puzzle says.) Making it even simpler, it means, "I am that man's father". Therefore, he is looking at his son.