I think that a good argument could be made that President Kennedy pursued the doctrine of flexible response in both crises. President Kennedy demonstrated that he was willing to negotiate through back channel diplomacy when warranted, and that he was willing to be hardline when the situation presented itself. President Kennedy did not lock himself into a doctrine that was so rigid that it failed to examine context and contingent circumstances.
In 1961 with Berlin, President Kennedy engaged in dialogue and communication with Khrushchev in order to avoid armed conflict and nuclear retaliation. This was one example of the flexible response doctrine. President Kennedy was able to do so without becoming mired in "Win vs. Lose" labels and perception. He understood that the timbre of the situation, given his time in office, required him to be a bit mindful of situations that might present itself later on in his tenure. One sees this understanding play out in 1962. In this setting, President Kennedy engages the Soviet Premier in a hardline stance of removing nuclear weapons from Cuba. Through White House Transcripts, it becomes clear that President Kennedy sought to understand all aspects of the situation, weighing out as many options as possible. However, it becomes clear that President Kennedy understood that there was a need to assert meaningful strength through flexible repsonse at this moment in assessing move and countermove on the part of the Soviets:
'A Soviet move on Berlin,' Kennedy said to the joint chiefs of staff, 'leaves me only one alternative, which is to fire nuclear weapons - which is a hell of an alternative.'
In 1962, President Kennedy understood that part of flexible response is being able to show strength and make hardline demands when such situations present themselves. In Berlin, he engaged. In Cuba, he demanded. For President Kennedy, the doctrine of flexible response carried with it the responsibilty to assert strength when needed.
It was here in which President Kennedy distinguished himself from members of his team who embraced "massive retaliation" through the use of nuclear weapons and his own understanding of interntional diplomatic nuances. Part of this was seen in the beliefs that President Kennedy and his team were agents of change in the world:
[T]hey carried with them an exciting sense of American elitism, a sense that the best men had been summoned forth from the country to harness this dream to a new American nationalism, bringing a new, strong, dynamic spirit to our historic role in world affairs… It was heady stuff, defining the American dream and giving it a new sense of purpose, taking American life… and giving it a new and grander mission.
The transformation from a massive retaliatory policy that envisioned American victory at the cost of submission of "the other" gave way to a doctrine of flexible response. Part of the reason that Hawks like General Le May were outnumbered was because of this "spirit" that majority of the President's Cabinet embraced.