This one is a good one. In certain situations you can use the singular noun “the eagle” in reference to the plural object or category of objects followed by a singular verb. “The sheep crossed the road” is typically taken as singular sheep, but based on context it can mean ‘all the sheep’ for example ”What happened to the sheep?” Would depend on the listeners understanding of whether this is a flock of sheep or just 1. So this lyric could be interpreted as the categorical “all eagles” which is correctly followed by the form “fly”. The way it is being used in the song is a bit more poetic and not something you would use in daily conversation where “eagles fly” would be much more natural.