Accidents "per flight" is unfair when comparing a 10-passenger Ford Trimotor
to an 853-passenger A380. Passenger miles is fairer.
Even fairer is accidents per passenger, ignoring miles,
because takeoff and landing have always been more accident prone than cruise.
But even easier to measure historically is fatalities per passenger.
Commercial airline travel as we recognize it started in 1926.
reports 36 fatalities worldwide that year.
1926 had about 6000 passengers in the USA.
Luft Hansa probably had more. Let's generously guess 20000 worldwide.
So the fatality ratio was about one in 550.
In 1930, 385,000 passengers were "carried on domestic and foreign airlines under the American flag". In 1935, nearly, 1,000,000 (Berkeley Daily Gazette). PlaneCrashInfo in these years veers away from airliners, though, and I couldn't find reliable global crash or fatality info for those years.
During World War II, and immediately preceding and following it, statistics about nonmilitary air travel are bound to be noisy.
From 1950 to 1970, per-year fatalities went from about 1,000 to 1,500
(with a dip in 1955).
Over that same interval, per-year passengers went from roughly 50,000,000 to 500,000,000.
So fatalities per passenger dropped from 1950 one in 50,000
to 1970 one in 333,000.
That second figure is corroborated by another source:
The "fatality risk per boarding" in 1968-77 was one in 350,000.
In 1978-87, one in 750,000.
In 1988-97, one in 1,300,000.
In 1998-2007, one in 2,700,000.
In 2008-2017, one in 7,900,000.
-- A. Barnett, "Aviation Safety: A Whole New World," Transportation Science 54(1), 2020.
summarized at http://www.sciencedaily.com/releases/2020/01/200124124510.htm