Draw a rounded line. I used a brush of about 7px here and a saturated orange.
Put the spark in one layer. Use blending mode "Linear Add". I added a gaussian blur of 2px.
Put the blured spark in another layer. Use blending mode Color.
My quick result:
P.S. Work in RGB mode.
Of course, it is not exact because I need to experiment with the brush color, but looks fine.
You can prepare this sparks as brushes or search for some online images for brushes: https://www.google.com/search?q=spark+brush
(Probably it is not a spark but burning ashes)
And the flares
New layer. Draw some simple strokes.
Motion blur, using a biiiiig value. I used 400px.
Use Screen blending mode.
I needed to duplicate several times this layer because with the blur it became very transparent (In this example is 6x). Layer over layer you will see the effect increasing. You can try blurring this layers in different ways/values but keep the same motion blur direction... or not.
You can do some variations on the initial brush strokes, so these elements will have different bright levels depending on how they combine.
You can play with blending modes, probably one of this layers can be linear Add or something.
I am totally sure this is not the only way, you could use some color masks or something to make this more "editable". I am not even sure if these blending modes are the best options. The point is to play with them!
Do you want to play with fire?
Take a look at flame painter: http://www.escapemotions.com/experiments/flame/index.php
This program uses this kind of accumulative blending modes. Probably will not be specific for this project, but it is an interesting option for "Light Effect".