More properly, he was a Marxist and the red in the Nazi flag was to appeal to Communists.
Mussolini had actually been a Communist. He was the editor of the Italian Communist newspaper.
More accurately, according to the book "Leftism Revisited" by Erik Kuehnelt-Leddihn, the original Nazi flags were actually made from communist flags that they already had because the Nazi party was formed from elements of the German Communists that already existed at the time.
They simply sewed a swastika over the hammer and sickle of the communist flags they already had.