The color nodes on the top are all you need to pay attention to. If you look, I've got a color ramp that I tried to use to get the sparks to shift color as they get older, but for some reason it isn't working correctly. The divide node seems to always be giving an output of 1, no matter what the age of the particle is. This means that the sparks only ever have the color of the very end of the color ramp. I've tried moving the left color picker over, even to within about 1 pixel of the right one. It has no effect and the sparks keep the color of the right color picker throughout their entire particle lifetimes. I did also make sure to actually give the particles a lifespan. Does anyone know why the divide node might be giving an output of 1? The age to lifetime ratio should start at 0 and progress to 1.
Here's a demonstration showing just that part of the cycles particle info being used to drive a colour ramp. Notice I had to also add in another divide just to get the far end of the colour ramp to appear in the view. You can see clearly that the individual particle blurred paths are constant in colour even though different particles may have different colours. You might be able to use a spherical gradient in addition to the age and lifetime values to change colour along a long thin particle to create the effect you are looking for.
Here's a crude version of the suggestion above.