Kissinger did not have a role in government until the Nixon appointed him National Security advisor in 1969.
He may not have had a role in government at the time the movie was made, but he certainly had a reputation as an international policy wonk among people in government for some time prior to his becoming NS advisor. It's not like Nixon found him working as a convenience store clerk and promoted him to National Security Advisor. Kissinger had a "behind-the-scenes" influence on American foreign policy for many years, and would have been known to the screen writers of "Strangelove" in the early sixties.
While it is possible that the character of Strangelove could well be someone else other than Kissinger, it is a stretch to claim that he is Teller, who isn't German, and who was here in the US working on the Atomic Bomb during WWII, not in Berlin giving der Führer fascist salutes.
A Commentary on Dr. Strangelove .
The case for Kissinger: he's German by birth, and the accent is very similar, which seems to be the main reason for linking Kissinger with Strangelove. Kissinger's subsequent career -- which journalist Christopher Hitchens compared to the pathology of a serial killer -- certainly matches Strangelove's ruthlessness. (Suggested reading: Seymour Hersh's The Price Of Power.) And given Kissinger's minor prominence and Kubrick's thorough research, one could argue it's likely that Kubrick thought of Kissinger.The case against Kissinger: In my opinion he was far too obscure a figure to be "parodied." One would want to parody a widely-known personage, and at the time, Kissinger was one of many theorists of the unthinkable.
The second favorite is clearly Werner von Braun, the former Nazi rocket scientist who quickly turned his services (and those of his underlings) to the U.S. after the war. In the Cold War, von Braun's expertise in rocketry was more important to the U.S. than prosecuting him for administrating slave labor at Peenemunde and Nordhausen. His books were written with a view to the future (I Aim For The Stars), but it was a theme in humor at the time to note Von Braun's earlier work (cf. Tom Lehrer's song about him, Mort Sahl's subtitle to his book ". . . but Sometimes I Hit London.")
The case for Von Braun: He was famous. He was German. He had been a faithful Nazi. He promoted a self-image of coldly rational theorization of pragmatic scientific realities, untempered by such human issues as compassion, morals, or values.
The case against Von Braun: Very little, apart from the fact that he wasn't a nuclear scientist, nor a theorist of nuclear deterrence.
A third runner-up is Edward Teller, the Hungarian physicist who worked on the atomic bomb at Los Alamos, and whose theoretical work was instrumental in developing the H-bomb. Teller was also willing to denounce Robert Oppenheimer as a security risk, thus ensuring his reputation among liberals as a scoundrel. He was also the man who convinced Ronald Reagan that the Strategic Defense Initiative was a workable concept. Even historian William Manchester, in the Oppenheimer passages in The Glory And The Dream, said that, eventually, Teller would be savagely parodied as Dr. Strangelove.
The case for Teller; His role in the Oppenheimer affair. His promotion of the development of the H-bomb. His continued role in promoting nuclear weapons development (he was the head of Lawrence Livermore labs for many years). He had a foreign accent that, to an untrained ear, might sound German.
The case against Teller; Teller was Hungarian, and fled the Nazis they overran his country.