If you'll forgive a pedantic response, the lesson here is that poetry (including the lyrics to songs) is elliptical, metaphoric, and allowed to violate the rules of standard English to conform to both the meter (or rhythm, if you prefer) and the imagination of the poet or lyricist. The interpretation of the associated meanings will thus be highly subjective. Let's see what can be teased from these lyrics:
We can fly away over
We can fly away over it all
Notice that the singer is singing her own counterpoint. There are two "sentences," and second interrupts the first. If we untangle the lyrics and supply some punctuation, we get
- We can fly away, over ...; we can fly away, over it all.
- You gave your hand, your heart, your all.
The first "fly away" is incomplete to make its lyrics fit the meter. The second "fly away" finishes that thought as it fits its own meter.
The sense here is "We can fly away and we can fly over it all." If it were phrased that way, though, it wouldn't work with the music. My insertion of commas should make it clear that the parsing does not contemplate "away over" as a syntactic unit, even if the intonation places the two words together.
This is a common aspect of English grammar, sometimes called zeugma, in which one word governs more than one syntactic unit. In this case, the word fly is modified by the adverb away ("fly away", meaning escape) and the prepositional phrase over it all ("fly over it all," meaning easily avoid all obstacles).
Notice that in the second sentence, the lyricist could have used zeugma to say
Your hand, heart, and all.
making the single word your apply to all three objects of the verb gave, but she deliberately rejected that to repeat the word your once for each object.
I fully expect that others might have a different interpretation, which is the natural state of things in the contemplation of verbal art.