Monty, as always: You got it (and I had thought with all those stroies about flying this would have been clear as to where to allocate it).
This is the German adaption (and nothing literraly translated) from the original you posted:
Those magnificent men in their flying machines,
They go up diddley up-up, they go down diddley down-down!
They entrance all the ladies and steal all the scenes,
With their up diddley up-up and their down diddley down-down.
Up! down! Flying around! Looping the loop and defying the ground!
They're all frightfully keen.
Those magnificent men in their flying machines!
They can fly upside down with their feet in the air!
They don't think of danger; they really don't care!
Newton would think he had made a mistake!
To see those young men and the chances they take!
Those magnificent men in their flying machines,
They go up diddley up-up, they go down diddley down-down!
They entrance all the ladies and steal all the scenes,
With their up diddley up-up and their down diddley down-down.
Up! down! Flying around! Looping the loop and defying the ground!
They're all frightfully keen.
Those Magnificent men in their flying machines!
Those magnificent men...
those magnificent men
Those magnificent men
in their flyyyyyyying machines.
All that was left in the German theme song of the film (of course, the only one I would have known in 1965) of the original was (and even today I dont know why really as it makes no sense whatsoever in German, obligation by contract, maybe?) were the two snippets "diddley down-down!" and "diddley up-up", I guessed that was enough info to allocate the song to its source (the movie: German title: "Die tollkühnen Männer in ihren fliegenden Kisten", I like the title translation better than the original title because it sets the spirit of the German version of the movie as follows: "Those death-defying men in their flying thingies" which, I guess you agree, sounds different and sure has a different impact on a 10 yrs old... Now as adult, I like the lyrics of the original better, but I stick with the German title...

).
Just to round it up, below the (also very distinct) lyrics of the German version (translated by yours truly), in the movie sung by the "Botho Lucas Choir".
Monty, 1 diddley up-up!

Just for the record, I have found some flaws in the movie that I can only charge to "continuity" department:
- German Colonel Baron Manfred von Holstein (impersonated by the unforgettable Gerd Fröbe: "... There is *nothing* a German officer cannot do!...Rumpelstoss, we go diving!...") and his aide Captain Rumpelstoss have
the same (wrong) rank insignia in their uniform: According to those they
both are of the rank of Major.
- When the German competitors first appear the today (and 1965) current German national anthem is played ("Einigkeit und Recht und Freiheit"):
http://www.youtube.com/watch?v=5q8xvkjqeHQ
This, in 1910, was the anthem of Austria/Hungary. Historically correct would have been the German Emperors anthem ("Heil dir im Siegerkranz") as National Anthem of the "Deutsches Reich" in 1910 (valid 1871-1918), but I guess they left it out of the movie as it has the same melody as the British "God save the Queen"... (oh, our European historical connections...!)
- The a/c that represents the "Demoiselle" (Santos Dumont) of the french competitor sports a 4 cylinder boxer engine from a VW beetle...
FWIW,
Rattler
Lyrics "Richt´ge Männer wie wir":
Richt’ge Männer wie wir, und der richtige Wind, / True men like us and a great wind
das macht Spaß, tiddeli up, in der Luft tiddeli down./ that is fun in the air (diddely....)
Richt’ge Männer wie wir, und ein reizendes Kind,/ True man like us and an appaling chick
das macht Spaß, tiddeli up, in der Luft tiddeli down./ thats fun in the air (diddeleys...)
Komm, und steig bei mir ein, / Come on, get on board,
Nichts ist so schön wie ein Flieger zu sein, / Nothing compares to be with an aviator
Nur wer wagt der gewinnt. / Only who dares wins
Richt’ge Männer wie wir, so im richtigen Wind. / like true Men in the right wind
So ein Looping ist schön, wenn es donnert und blitzt, / A looping in a thunderstorm is the greatest adventure
Was kann schon gescheh’n, wenn Du dicht bei mir sitzt. / nothing can go wrong if you sit by my side
Rund um die Welt, das ist gar nicht sehr weit, / All aorund the world really is tiny a distance
die Vögel im Wald, ja, die platzen vor Neid. / The birds in the woods explode from envy to us
Richt’ge Männer wie wir, /True Men like us
Richt’ge Männer wie wir, /True Men like us
Richt’ge Männer wie wir, /True Men like us
So im richtigen Wind./ In just the right wind