Get this letter and response from Superman #141 (November 1960):
It was indeed an excellent request, and yet despite Weisinger's promise, nothing came of the Superman-Flash race for almost seven years.
Finally, in Superman #199, the race came off. Supes and the Flash agree to a race for a UN benefit, with a "sweepstakes" (i.e., legalized wagers). One very interesting aspect to the race was that it emphasized the difference between Superman and Flash's powers, even though this was nominally a footrace. Superman was able to beat the Flash in some places, but when it comes to the sand dunes of the Sahara, the Scarlet Speedster has the advantage:
Making the race a little more interesting is that a US crime syndicate has bet on Supes, while a European cartel has bet on the Flash. This seems to be a swipe. Some may not be aware that there was another iconic series of races in American pop culture; in the early 1940s, Warner Brothers produced three separate cartoons featuring the Tortoise (Cecil B. Turtle) Against the Hare (Bugs Bunny), and oddly enough, the storyline for the second instalment, Tortoise Wins By a Hair, includes a subplot of gamblers sabotaging one of the racers:
And such was the case here:
Hilariously, though, the other syndicate has laid out the Flash as well, and substituted a ringer. Given the order for both of them to lose, the inevitable happens:
But in the meantime the two heroes have freed each other and they rocket towards the finish line, where they carefully break the tape together, in order to foil the gamblers (and presumably the sweepstakes ticket holders as well).
The rematch came in Flash #175. A pair of alien gamblers want the race rerun, and this time they add a little incentive: If the Flash loses, Central City will be wiped out, whereas if Supereman fails Metropolis will be leveled. Despite this, both heroes find themselves helping each other overcome obstacles. Predictably, perhaps, the outcome is inconclusive:
We learn that the two alien gamblers are actually the Reverse-Flash and Abracadabra, who have set this up in order to unleash some death traps at the Central City Comet, but they are eventually foiled.
The rubber match came (appropriately enough) in World's Finest #198-199. Superman is summoned to Oa by the Guardians, who advise him that a race of faster-than-light robots is moving through the galaxy and the only way to prevent them from destroying the time/space fabric is for Supes and the Flash to run in the opposite direction. This time the race will take place in outer space, so they give the Flash an amulet which protects him and also creates a track for him to run on.
The alien robots turn out to be a plot by the Phantom Zone criminals to escape from their prison. Superman and the Flash are wounded, with their legs useless, so they must crawl to a control room to turn off the robots:
And in the end, the story doesn't cop out:
It's hard to believe Weisinger would have allowed this during his reign as editor, but Julius Schwartz had taken over the reins of World's Finest effective with #198, and Schwartz was naturally a Flash partisan, having guided the Scarlet Speedster since his initial (Barry Allen) appearance in Showcase #4.