First off, song lyrics typically fall on the poetry side of the poetry/prose divide and sometimes bend grammatical rules in the name of aesthetics or emphasis. Having said that...
When I listen to this song, I hear the missing word as “I’ll”, not “I”. That would make the revised sentence:
[I’ll] make my way home when I learn to fly.
This sentence is in the first conditional, which does express whatthe meaning you’re thinking it doesexpecting.
I think the primary reason I’m interpreting thisto interpret the sentence this way is that people generally learn to fly only once, so it can’t be a habitual action that would use the zero conditional.