Kyle Richmond, the Nighthawk of the classic Squadron Supreme of Earth-S (alias Earth-712), died in Squadron Supreme #12 in the 1980's and remained dead. His ward, Neal Richmond, became the new Nighthawk of Earth-S and appeared with them occasionally in places like Exiles and Ultimate Power.
Kyle Richmond, the Nighthawk of Earth-616's Squadron Sinister, quickly reformed and become one of the longest-running members of the Defenders. Following Civil War, he retired and named a successor, S.H.I.E.L.D. agent Joaquin Pennysworth, but was also seen back in costume around the same time. Neither of them have appeared since 2011.
Kyle Richmond, the Nighthawk of Supreme Power's universe, was folded into Earth-616 following Secret Wars. Also known as Raymond Kane in this reality, he served with Earth-616's Squadron Supreme, made up of Squadron-like refugees from various timelines. He began working with the former super-villain Deadly Nightshade as his tech support. Following Occupy Avengers and the Secret Empire tie-ins, Nighthawk was killed (I think even behind-the-scenes), and Nightshade became the new female Nighthawk...until the end of that series, after which the development has been ignored.
Kyle Richmond, the Nighthawk of the Squadron Supreme of America, was introduced in the current volume of Avengers. He sits as house representative for the District of Columbia in Congress. His (their) origins are somewhat unclear. The SSoA were established by Mephisto's pawn, the resurrected Phil Coulson, in conjunction with Thunderbolt Ross, working for the Power Elite seen in the last Captain America series. They may be nothing but constructs or simulacrums, living archetypes designed to appeal to "The American Way" as being sold to the public by the Elite and Mephisto. Their personalities were being programmed and controlled from afar in their earliest appearances, apparently by a scientist support team run by Coulson. When Coulson used the Pandemonium Cube to create the Heroes Reborn reality, the Squadron replaced the Avengers as the horrifically brutal and fascist heroes of that reality. They recall those events after reality reverted but, like Evil Steve, believe their reality was the REAL one, and the genuine 616 is the fake.
"If you want to tell people the truth, make them laugh, otherwise they'll kill you." -- Oscar Wilde