Mostly superheroes do not need cars because of webs and powers and so on. Even the Batmobile really only made sense back when it was introduced in 1939, because only about seven people had cars then. You could park a big black car with a bat on it anywhere then. But there is really no reason for the Flash to have a Flash car, unless the Flash wanted to go much slower that day, or he had a bunch of luggage to take with him while crime fighting.
