You can read Robert A. Caro's "The Passage of Power" for a moment-by-moment breakdown of this. It took about two hours after Kennedy was shot for Johnson to be sworn in, and the plane was not particularly chaotic (although it was very hot).

The rough timeline: Kennedy is shot at 12:30pm Dallas time, the motorcade diverts to Parkland Memorial Hospital, where the excellently-named Secret Service Agent Rufus Youngblood sets up LBJ in a hospital room 'cubicle' until more information can be gathered.

At 1:20pm Johnson is told by Kennedy Aide Kenneth O'Donnell that Kennedy has passed. At THIS point, Johnson has become President. He doesn't actually need swearing in. It is a seamless transition of power, although Johnson, as a keen and astute political player, is aware of the visual and theatrical impact necessary to facilitate the transfer of power.

Johnson quickly left the hospital with Rufus Youngblood and other agents under armed guard, Lady Bird Johnson leaving in another car, as the assassination event had not been fully locked down and determined yet. Johnson's one friend in the Kennedy family had always been Jackie, and he quickly arranged for a photo op/swearing in ceremony on the stifling plane, which, lying on the tarmac, did not have the chance to utilize the air conditioning. Johnson, additionally, in an act of almost unconscionable political cruelty, called and asked Bobby Kennedy (whom he loathed), the exact phrasing of the oath of office he would need to take to assume his newly-deceased brother's office.

Johnson, additionally, refused to leave JFK's body and casket were aboard Air Force One. He was quickly in command an found a political ally in Texas, judge Sarah Hughes, to swear him in (a task almost entirely performed by the Chief Justice of the Supreme Court). Things were somewhat tense, but not chaotic enough for Lyndon Johnson to settle a personal score between himself and Bobby Kennedy, await Jackie Kennedy to stand by his side (and her request that JFKs body get aboard) during the photograph of the swearing in. From actually become president at 1:20 to gathering the necessary people, the former president's body, getting a federal judge, and coordinating a swearing along with a famous photograph, took just under 90 minutes. Caro's book makes it very clear that once he is made aware that Kennedy is dead and that he is president, Johnson is very much in charge, in command, and has very little doubt of the way forward, resulting in very little chaos between the hospital and takeoff, and between takeoff and the rest of the day.