I can't answer the question, but I can possibly address a misconception which might have led to the question. Kaliningrad is part of Russia, which isn't the same as the Soviet Union. The USSR was made up of a number of constituent republics, of which Russia SFSR was one of them. However, Lithuania - which Kaliningrad abuts - was not an independent country at that time, but another constituent part of the USSR. I can't speak to why Kaliningrad was made part of Russia SFSR and not Lithuanian SSR (/u/facepoundr maybe?), but prior to the breakup of the Soviet Union, Kaliningrad, while an enclave of Russia SFSR specifically, was not outside of the USSR proper, simply on the edge.

So while NATO might have had some specific plans for dealing with Kaliningrad, it wouldn't have been due to it being separate from the rest of the Soviet Union.

During the Cold War, Kaliningrad was still contiguous with the USSR. Latvia, Lithuania and Estonia had been annexed by the USSR in 1941, a state of affairs which continued until 1991. Along with the rest of the USSR proper, it was buffered from NATO by the Warsaw Pact states. To threaten it, NATO would have had to have fought through East Germany and Poland. As a result, Soviet plans for its defence were essentially those for the defence of the Warsaw Block in its entirety. The Soviet plans that have been released have focussed on conventional attacks in response to a NATO nuclear first strike - they assume that NATO will nuke logistics and transport targets in Poland and Eastern Europe. The planned response was to nuke similar targets in Western Europe - major ports and rail centres in particular. Warsaw Pact troops would then advance across the border in force, destroying NATO forces opposing them, and making fast advances deep into the West. One published timetable has troops reaching the Rhine in 7 days, although this was seen as optimistic. NATO plans haven't been released, but would likely focus on defeating Soviet thrusts into the West. Counter-attacks would then take place. These attacks would result in either a negotiated peace along the pre-war border, or a full-on strategic exchange.

Today, with Kaliningrad as an enclave, it would be much harder to defend, and very difficult to use as a base for offensive actions. I'd assume that Russian forces in Kaliningrad would have a similar role to NATO troops in West Berlin in a Cold-War-Gone-Hot scenario - both would ultimately fall, but they would distract units from the main fighting. Aircraft and ships based from Kaliningrad would be useful to harass nations with a Baltic coastline, but these would be easy to shut down.