General movement:
* Dart
* Flutter
* Glimmer
* Glide
* Hover
* Scud
* Skip
* Soar
* Swerve
* Whirl
Short-lived or fleeting:
* Pass
* Vanish
* Disappear
* Evade
* Dodge
To move quickly and lightly:
* Skim
* Skip
* Hop
* Leap
* Bound
To move from place to place:
* Wander
* Roam
* Travel
* Migrate
The best synonym will depend on the specific meaning and context of "flit" in your sentence.