Correction: Wenn hinter fliegen fliegen fliegen, fliegen fliegen fliegen nach.

It's actually quite sensible in German. Transliterated, it's "When behind flies flies fly, the flies after-fly the flies." Translated it would be more like "When flies fly behind flies, flies are following flies."

To "after-fly" is to follow, but by flight. And of course, per usual in German, that verb is split apart with the "after" prefix stuck at the end, which is how you end up -- quite naturally! -- with six fliegens in a row.

Confer this gem from Mark Twain's "The Awful German Language":

The Germans have another kind of parenthesis, which they make by splitting a verb in two and putting half of it at the beginning of an exciting chapter and the other half at the end of it. Can any one conceive of anything more confusing than that? These things are called "separable verbs." The German grammar is blistered all over with separable verbs; and the wider the two portions of one of them are spread apart, the better the author of the crime is pleased with his performance. A favorite one is reiste ab -- which means departed. Here is an example which I culled from a novel and reduced to English:

"The trunks being now ready, he DE- after kissing his mother and sisters, and once more pressing to his bosom his adored Gretchen, who, dressed in simple white muslin, with a single tuberose in the ample folds of her rich brown hair, had tottered feebly down the stairs, still pale from the terror and excitement of the past evening, but longing to lay her poor aching head yet once again upon the breast of him whom she loved more dearly than life itself, PARTED."

Shouldn't there be time and arrows in there somewhere?

Time flies like an arrow; fruit flies like a banana.

Time flies like an arrow; space flies like a bow.