If Mussolini escapes into Switzerland, I would imagine some fascist sympathizers in Switzerland would find a way to get him into Spain (And I imagine that the Swiss would probably turn a blind eye if bribery is involved). If Mussolini gets to Spain from there (Likely by plane, identified as being from a neutral country), I imagine that Franco would shelter Mussolini, at least temporarily. Franco, despite probably being one of the smarter dictators in the 20th century, would probably have some admiration for the man and shelter him in a monastery somewhere in Southern Spain.
I imagine that once things settle down and the Cold War starts up (Probably 1948-1950 range), Franco would probably have Mussolini smuggled into South America, likely in Brazil or Argentina. Mussolini grows facial hair and probably loses a lot of weight over the years, so he will probably look a bit different, and isn't as notable as Hitler in South America. Now, Mussolini had multilingual skills. He could speak Spanish, French, English, and German alongside with his native Italian, so I could imagine he would probably return to teaching in a small and obscure town while writing his memoirs.
If Mussolini isn't caught, he'd probably die by the 1960s, and his death would probably be found out by the late 1960s or early 1970s as his memoirs he has been writing are published. We get a more in depth account than he already gave (In his memoirs, My Rise and Fall, written during his rise to power as well as during his final days), so we can probably have a better understanding of his actions. I imagine though that if Mussolini lived, fascism might be a bit stronger, especially if he has new writings published after his death.
Of course, this all assumes that he isn't arrested at the airport in Switzerland or isn't turned over by Franco upon landing.