Yes, Nightwing and Flamebird were the non-powered "Batman and Robin-like" identities frequently adopted by Clark and Jimmy within Kandor during the pre-Crisis era.
Dick adopting the name was a perfect tribute of Superman and Batman, honouring the two heroes who had shaped the man he'd become.
Of course Crisis buggered that up for 10 years, since Kal had never been a hero in Kandor... and Superman and Batman hadn't been colleagues...