The cartoon follows the story of a B-29 Bomber named John (voiced by Daws Butler), who is married to a Douglas DC-3 named Mary (voiced by June Foray). John can't seem to find work at any airport because they're looking for jets. Mary later reveals that she's going to have a baby, and needing to find work to support his family, Johnny heads off to reenlist in the Air Force, but finds even they won't take him back in, as they're looking for jets as well, which further angers him. When Junior finally arrives, John's happy to have a child...until it turns out that Junior is a jet as well, which makes John lose his mind (but he doesn't take it out on Junior).
When reading the paper the next day, the Hot Air News, John sees the ad for a jet contest held by the United States Government where the winner gets a huge contract. Plenty fed up with jets, he goes to enter the contest as well to try to show them up. Realizing that risk that her husband is putting himself, Mary (with Junior in tow) goes after John. En route to the contest, John meets a B-29 general who smokes Douglas MacArthur's trademark corncob pipe and has Bataan written amidst his five stars. When John asks him, the general declines to enter the contest and states, parodying MacArthur's farewell address to the U.S. Congress, that "older planes never fly, they just fade away," before literally fading away.
At the contest, John lines up at the starting line with the rest of the jets. Mary and Junior catch up to him and Mary tries convincing John not to go through with the race, but John refuses to listen to her. While this was happening, Junior gets out of the baby buggy and gets in the fuselage of John, and by the time Mary realizes that her son's there, it's too late.
At the green flag, the jets all but disappear while John, in comparison, sputters badly to take off and run the race. Within no time, his engines had had enough and detach from his body and fly away on their own, sending him into a nose dive for Earth. Junior realizes what's happening and after a brief struggle with the door, manages to get out of him in time to grab him by the tail and save him. When John notices that he hasn't crashed, he looks back and sees his son holding his tail and flying him along. After happily praising him for saving him, they then kick it into high gear and run the race, tearing past the other contestants (freaking them out in the process), and are shown flying around the world, going by certain landmarks with funny things happening (the Eiffel Tower pulling itself open to let them through, the Leaning Tower of Pisa tilting the other way, they fly by a huge cloud of smog which is completely removed to reveal Los Angeles, The Statue of Liberty's dress blows open to reveal then-rather risqué lingerie on her (leaving Junior perplexed), etc.), and a few non-landmark things as well (a blimp gets cut in half to look like a watermelon, a sky-written ad for a cola changes to read "BURP!", an ocean liner gets shrunk down to a tugboat, and a rainbow literally tied up like a bow, etc.).
They easily win the race and the government contract...for Junior. While John's happy for his son, his joy is soon (somewhat) crushed when the government tells him that they need ten-thousand more just like him—John realizes that he and Mary have some serious procreating to do.