You realize the origin is only that complicated because you made it that way. Her previous origin was she was a Supergirl construct who merged with a dying girl in order to save her life, and became an earthborn angel with flame powers. Then she was just Linda Danvers with Superman's powers and Tk.
If you introduce her as Flamebird, all you have to understand is "This was the Supergirl with flame powers. Now she's Flamebird.
I'm not saying I'd have wanted her to have the same origin as Thara, but that I originally thought that Flamebird was going to be Linda and that would have been a good way to bring her back, and I still think it would have been better than having Thara have almost the same powers redundantly.