Could you please post your image at 1200 pixels on the wide side and all the techs as well?
It's a Silvereye by the way, a Zosterops sp, not a finch.
We have them in Oz, but yours I think is not the same species.
As mentioned by Akos, we can better critique a full size image, details easier to see, but I do think you in fact are on the right track about using fill flash. That tech. will allow you to shot in the shade and compensate somewhat for the bright backgrounds that are so common. I often shoot a short series with flash bracketing to try and fine tune the result. Goal is to get some light on the subject without it looking overly 'flashed'
Seeing the techs now posted I do think f/14 was a bit much and made the BG worse. Photographing wide open, or close to it, would have more than likely smoothed out the BG to a much more pleasing result. Great looking bird though, and the flash work is nicely done.