
verfliegen
to fly by
To pass very quickly, especially in relation to time.
Die Zeit im Urlaub ist wie im Flug verflogen.
The time on vacation flew by.
to fly by / fade away
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to fly by
To pass very quickly, especially in relation to time.
Die Zeit im Urlaub ist wie im Flug verflogen.
The time on vacation flew by.

to fade away
To dissolve and disappear, especially with smells, feelings, or moods.
Der Duft des Parfums war nach wenigen Minuten verflogen.
The scent of the perfume had faded away after just a few minutes.

to lose one's way
To lose orientation while flying and go off course.
Die Brieftaube hat sich bei dem Sturm wahrscheinlich verflogen.
The carrier pigeon probably lost its way in the storm.
'Verfliegen' is an inseparable verb made up of the prefix 'ver-' and the verb 'fliegen' (to fly). The prefix 'ver-' indicates here that something disappears or gets lost.
Der Zorn des Vaters war zum Glück schnell wieder verflogen.
Fortunately, the father's anger had quickly faded away again.
The perfect tense of 'verfliegen' is always formed with the auxiliary verb 'sein', because it describes a change or disappearance. So it is 'die Zeit ist verflogen' (the time has flown by), not 'hat verflogen'.
Der schöne Sommertag ist leider viel zu schnell verflogen.
Unfortunately, the beautiful summer day flew by much too quickly.
When talking about time, 'verfliegen' (to fly by) is often combined with 'wie im Flug' (as if in flight) to emphasize speed. Typical subjects are 'die Zeit' (the time), 'die Stunden' (the hours), or 'der Urlaub' (the vacation).
Die drei Wochen Sommerferien sind wie im Flug verflogen.
The three weeks of summer vacation flew by.
The reflexive form 'sich verfliegen' has a very specific meaning: a flying living being or object loses its orientation. This meaning is always reflexive, unlike the other meanings.
Der junge Vogel hat sich im Sturm vom Schwarm getrennt und verflogen.
The young bird got separated from the flock in the storm and lost its way.
to disappear
With smells, feelings, or moods, verschwinden and verfliegen can both describe their coming to an end. Verschwinden generally says that something is no longer there. Verfliegen describes more specifically how it gradually dissolves.

Nach dem Lüften verflog der Rauchgeruch langsam.
After airing out the room, the smell of smoke gradually faded away.
Nach dem Lüften verschwand der Rauchgeruch vollständig.
After airing out the room, the smell of smoke disappeared completely.