We can take advantage of the facts that
- flames are lighter than the background
- the background is a horizontal gradient
So let's go:
With the rectangle select tool, select this small zone (I added vertical guides to help move the layer later, but that's not mandatory)
Apply a gaussian blur filter, configured like below. Important: check "Merge filter"
Layer > Scale layer. Scale it only vertically by unchecking the chain icon first:
With the move tool, place the layer above the lights:
Set the layer to "Darken only" mode:
With the eraser tool and a rectangular brush, erase the pixels over the candles bodies (wax only, not the flames):