I'm not confident (edit: I'm pretty confident after writing the answer), but it's close enough to try.
Free Bird, the song by Lynyrd Skynyrd
Some of these are lyrics references, the yeah yeah and Oh oh oh oh inspired this answer.
I am the cheapest of the flying animals,
As such I cannot give any change.
"'cause I'm as free as a bird now, and this bird you cannot change"
I guess I am just riffing yeah yeah,
He sings "yeah yeah" after a few different lines to my recollection. Perhaps also right at the solo.
But I heard my creator is "too too wise".
No idea. Either a reference to "Lord" in the song or the band (creator) Lynyrd Skynyrd? The song is legendary.
Anyways I will just soar above, won't I,
Oh oh oh oh, you realize I must go.
"Won't you fly high, free bird" and some "oh"s in the verses.
My stay has been sugary, but bye.
"Bye, bye, baby. It's been a sweet love."
VERY late edit: I heard the opening credits of Happy Gilmore this weekend, which instantly reminded me that I never responded to the riddle's hints.
My brother is a man least complex
Another song by Lynyrd Skynyrd is Simple Man
As well as a day lost to the breeze
The chorus of Tuesday's Gone is "Tuesday's gone with the wind"