There appear many pages about Frane Selak, but none of these pages give more details about that particular accident, or any of the accidents that he was involved in. Plane accidents are very well documented on several sites. If you look at the year 1963 at PlaneCrashInfo, there is no mention of a crash that involved 19 deaths and one or more survivors. Digging further, there appears to be no crash record that mentions loosing a door during freefall (there is at least one mentioning an opened door in 1989, but not in 1963).
I am not saying it is impossible to survive such a fall, weird accidents and survivals happen, but I would say that his story is fabricated, or if not, badly documented (maybe the year or amount of fatalities mentioned are wrong, but I tried other years and fatality numbers, but found naught). But what really seems to point into the direction of fabrication is the lack of detail: what airline, what country, what flightnumber was the incident? None of the stories mention it and the journalists don't seem to bother.
Apart from the aircraft incident, it will be hard to prove or disprove the other incidents, as they are too small and too long ago to have made it into public records. One note on the train incident: it seems severe enough it would have made it into this list, but nothing of the kind can be found there.
Update: this article claims the flight was from Zagreb to Rijeka and this article from 2004, asking the same questions as you on Selak's story, claims it was a DC-8. In the same thread, a user claims that "No DC-8s have been lost between Zagreb and Rijeka, in 1963 or any other year.". None of the DC-8 accidents, or Zagreb accidents, seem to have any relation to this story.
Update 2: a person going by the name Jayco (Zeljko) Selak claims to be his father and invites you to ask him personally in another comment. He says that Frane Selak deliberately fabricated the story in an interview with a journalist from The Scottsman, which has since been printed and reprinted over an over. Quote from the link (in case the link goes dead):
Than in his old age he got lucky and won a lottery.That wasn’t enough for fame…So he has found (and paid?!) a local “journalist” to fabricate the story in the local newspaper about incredible death-cheating life! Some naive scotish “jounalist” saw the story and (without checking the facts!) has published the story in “The Scottsman”!
Of course, without verifying whether he truly is his son, or without checking with Frane Selak himself, there is no way to truly dismantle this story. However, if you sum it all up, it is pretty sure it is all made-up and fabricated, except for winning the lottery.