BRAVE AND THE BOLD #67 came out on July 28, 1966. With a script by Bob Haney and art by Carmine Infantino, it was the first Flash/Batman team up (other than in the JLA).
The premise: Batman is sad because he can’t stop the sneaker bandit kids who run really fast. (They’re actually called the “Speed Boys,” which would be quite the double entendre for a more modern criminal gang.)
Batman asks for help from the Fastest Man Alive, whose speed is actually killing him. And in the end being bitten by a radioactive sneaker seems to help Flash.
Classic Golden Age Cheese.