Beatification and canonization process requires the demonstration of miracles performed by the person being considered for sainthood. I don't believe Kennedy has any attributed to him.

The process of canonization for President Kennedy was never begun.

Miracles are not required for the canonization process to begin, that is only required for the process to move forward (and only in non-martyrdom cases). For the process to begin, the bishop where the person died can petition the Holy See to begin the process (I don't know if the death location takes precedence over the person's home diocese, but it appears not to according to Article 21 of this document, so the process would be begun by the Bishop of Dallas). The goal of this petition is to receive a nihil obstat--nothing stands in the way--from a group of Vatican organizations (especially the Congregation for the Defense of the Faith as well as the Congregation for the Causes of Saints). If that is approved, then the local diocese can begin the process. The process is long, and there are four steps--not two. The steps before beatification and canonization result in the individual possibly being declared a "Servant of God" and then possibly advanced to the title of “Venerable”). For instance, Pius XII--the subject of my flair--is “Venerable”. Only after those two steps have been completed can the process move forward to beatification and canonization (with the exception of equipollent canonization discussed briefly below) So despite not yet being beatified, the process has already begun.

Had it begun shortly after his death in 1963 JFK's cause would have straddled two different procedures, as Paul VI changed the procedures for beatification in 1971. Since the standard wait is a minimum of five years after the individual's death, the older procedure would have held for 1968-71, and the newer procedure afterwards. Regarding miracles, there are two different standards. If the cause is attempting to prove that the individual was an example of of heroic virtue a miracle would indeed be required—and a second one for the canonization step (previously four, prior to changes by John Paul II in 1983). This requirement of a miracle for beatification to move forward is not present in causes that are for martyrs. Also, pontiffs can and have waived portions of the process via “Equipollent canonization.” This waiver itself has a number of requirements, particularly that a local population has venerated the individual since their death. This would be difficult to assert in the case of JFK on a religious level, though the secular veneration of his life is considerable (but not applicable).

Also in the case of JFK, one would have to decide to pursue the process either via heroic virtue or martyrdom. In either method, a positio would be created, which is a specialized biography that includes as much information as possible on the individual in question (including their speeches and documents, as well as interviews and sworn testimony).

If you want to read about the process, the current procedures are available here from the Vatican. These procedures would apply since the process has not yet begun (and would constitute another hurdle, as the delay between JFK’s death and the initiation of the process would have to be explained). It is a rather detailed document. For a more readable synopsis, this explanation from a Catholic website might do the trick. For something in the middle, this entry from the Catholic encyclopedia is accurate. As stated above, so far as I know this process has not yet begun and could only be short-circuited by equipollent canonization—which is so much of a long shot that I cannot adequately describe how remote that possibility is. I know of no movement that is pursuing this concept.