The characters of Nightwing and Flamebird in the DC universe have a bit of a complicated back story, with at least half a dozen separate characters taking on each of those names. For example, the Nightwing and Flamebird that are currently the focus of Action Comics not that Superman is off in New Krypton bear no relation to the Nightwing of the Batman comics, which is the costumed identity of Dick Grayson, the first Robin(although he was inspired by the characters, who were inactive at the time he chose the mantle). Basically the names Nightwing and Flamebird are archetypal, and many people have taken over the mantle in order to give a symbolic weight to their heroic antics.
But that's not how the characters first saw light way back in the early sixties.
In the Superman comics of the 60s and 70s, Supes and his pal Jimmy Olsen had a series of adventures in the Kryptonian city of Kandor, which had been shrunken down and bottled by the villain Brainiac. In this miniature city Superman had no superpowers, and through some weird misunderstanding he was branded an outlaw, so he fashioned himself a new identity based on a bird native to Krypton; Nightwing. Jimmy Olsen joined in as Flamebird, and together they became a famous vigilante duo, fighting crime and righting wrongs.
The implication is clear: Superman's secret desire is to be Batman, and he roped Jimmy Olsen into his role-play fantasies as his own Robin. This is a theory pretty much confirmed by the comic itself; the persona's of Nightwing and Flamebird conform to the Batman and Robin iconography, with Nightwing in all black and Flamebird in bright oranges and yellows. Instead of a Batcave they have a Nightcave, and a Nightmobile instead of a batmobile. If that wasn't explicit enough, Superman chooses the name Nightwing because there are no bats on Krypton, so the name Batman would just confuse people.
But wait, there's more!
In post-Crisis continuity(for the non-comic nerds, Crisis on Infinite Earths was an event that spanned every DC Comics title in the mid-eighties, ending in a massive rewrite of the continuity up to that point, in an effort to streamline the comics and in some ways start from scratch) Nightwing and Flamebird were re-written as part of the Kyrptonian creation myth. Nightwing and Flamebird are part of a trinity of servants to Rao, the Kryptonian god(the third servant would be Vohc, the Breaker). Each generation, the essences of Nightwing and Flamebird are reborn in two individuals with a great love for each other that is doomed to end tragically in death.
I'm not quite sure how Jimmy and Supes fit into that equation.