Unfortunately, (as mentioned in the linked thread), this issue is a bug.
There is a workaround however, which isn't ideal or 100% polished, but its a quick and dirty method to get the job done.
1. As you can see in the screenshot, I have the same issue (Note: This bug only applies to the 'Fire' flow type, the 'Fire & Smoke' type renders without issues).
2. Begin by ensuring that
Transparent is checked under
Film in the Render Properties Panel, and also that the PNG Type is set to
3. Next add a large plane behind the fire object. Ensure that it is wider than the bounds of the camera and is far enough back from the fire object as not to cast light onto it. Give it a simple deep blue emission shader, with strength set to 1. (Note: I've noticed a bug here in 2.74 whereby if there is an object behind the viewport display of the smoke and fire, it wont dispay properly. Don't worry though, this doesn't seem to affect the renders.)
4. Render the image and jump on into the
Compositing Screen Layout. Check the
Free Unused, and
Backdrop boxes below the Node Editor, and add in a
5. Hit Shift+A and go Matte>Keying, add this to the Node tree.
6. In the
Key Colour setting, use the Eye Dropper tool to sample the blue from the original render, this will mask out all hues from the render which display the selected colour. If the blue appears black, it's likely that you don't have the
Use Alpha check-box ticked on the
7. This should update the render automatically in the bottom left
Image Editor. If it has simply hover over the transparent render and hit F3. If not just give it another render, ensuring that the
Compositing check-box is ticked under the
Post Processing tab in the Render Properties Panel, and it should display the composite fine.
Et Voila, the final render! :) As I mentioned it's not a perfect solution, and where the blue was subtracted from the edge of the flame it has become slightly pink tinted, but for all intensive purposes it works okay, and colour correction could be applied either in Blender or in Photoshop/Gimp. Finger's crossed the bugs'll be fixed in the next release.