Capone fled to Chicago because he had to. Police were after him for two murders, and an Irish gang, the White Handers, were hunting him for beating up one of their members. He probably would have been killed or gone to prison had he remained in NY.
Keep in mind that Torrio was no more than a well-connected ward heeler in Brooklyn before he moved to Chicago. There was far more opportunity for non-Sicilians like Torrio and Capone in Chicago than in NY at that time. The Outfit under Torrio and Capone wasn't a Mafia family, and included quite a few well-placed members who weren't even Italian.
