
fliehen
to flee
To move quickly away from a place or person in order to escape danger, a threat, or coercion.
Wegen des Krieges mussten viele Menschen aus ihrer Heimat fliehen.
Because of the war, many people had to flee their homeland.
to flee
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to flee
To move quickly away from a place or person in order to escape danger, a threat, or coercion.
Wegen des Krieges mussten viele Menschen aus ihrer Heimat fliehen.
Because of the war, many people had to flee their homeland.

to escape
To avoid or try to escape an unpleasant situation, a feeling, or reality.
Er flieht in die Arbeit, um nicht über seine Probleme nachdenken zu müssen.
He escapes into work so he doesn't have to think about his problems.

to fly by
(elevated, literary) For time: to pass quickly.
Im Urlaub schienen die Stunden nur so dahin zu fliehen.
On vacation, the hours seemed to simply fly by.
Since 'fliehen' (to flee) describes movement away from a place, the perfect tense is always formed with the auxiliary verb 'sein' (to be). A common mistake is using 'haben' (to have).
Die Familie ist vor dem Krieg in ein anderes Land geflohen.
The family fled to another country because of the war.
'Fliehen' (to flee) is often used with two prepositions: 'fliehen aus' + dative describes the place one leaves, and 'fliehen vor' + dative describes the danger one is escaping from.
Er ist aus dem Gefängnis geflohen.
He escaped from prison.
The verb 'fliehen' (to flee) is the basis for the nouns 'die Flucht' (the act of fleeing/escape) and 'der Flüchtling' or 'die Flüchtende' (a person who is fleeing).
Die Flucht über die Grenze war sehr gefährlich.
The escape across the border was very dangerous.
In a figurative sense, you can also 'in' etwas fliehen (flee into something), with the accusative. This expresses that you withdraw into an activity or state in order to escape reality.
Sie flieht oft in ihre Fantasiewelt, wenn sie traurig ist.
She often escapes into her fantasy world when she is sad.
When 'fliehen' (to flee/fly by) is used in relation to time, it is an elevated, poetic expression. In normal usage, you would say that time 'vergeht' (passes) or 'rennt' (runs/flies).
Die Zeit schien nur so zu fliehen, während wir im Urlaub waren.
Time seemed to simply fly by while we were on vacation.
to pass / fade
Fliehen and vergehen can both express that time passes quickly. Vergehen is the neutral and usual choice, whereas fliehen sounds elevated and literary in this sense. Use vergehen in everyday situations and fliehen mainly in poetic or narrative texts.

Im Gedicht heißt es, dass die Stunden lautlos fliehen.
The poem says that the hours fly by silently.
Während wir reden, vergehen die Stunden sehr schnell.
While we talk, the hours pass very quickly.