I know that they're a decorative item like textures but can someone explain to me a little better how they work in general?

I'll give it a shot.
Flames are created in the flame forge ingame.
Flames are specific to a body part. This is chosen when they're forged.
Flames will appear to burn and give off particles. The rate of this along with other specifications of the burn (size, density and all that) are also chosen when the flame is forged.
Flames offer no true gameplay advantage. Sometimes they might lag a slower computer or be a distraction to the enemy however.
Flames can be disabled with /opt flames
The 'look' of the particle can be changed by buying a flame particle texture. Depending on the color of the texture it may also change the color of the flame.

Feel free to add on or correct stuff.

./opt particles 0 for disabling them ingame.

You can buy flame textures and put in pictures to have your flame release those pictures instead of 'fire'

Ok, thanks guys!

Adding to what solax said...

You can only change the color of VOID (black) flames with the use of a particle texture. It doesn't work for every flame which is primarily part of the reason why void flames are more expensive than other colored flames.