My grammar book says that 'over' is used for horizontal movement at a higher level.

The helicopter is flying over the sky.

Is this correct?
I think It may mean the helicopter is flying at a higher level than sky, which could be stratosphere by stretch of the meaning of 'over'.

Is there better prepositions here?

Alternatives could be "across" or "through".
In one sense, if you think of "the sky" as a two-dimensional blue sheet overlaying the world, a helicopter could be flying over it [on the world's side of the sheet].
Got it! Thanks, Feebs.