##Don't use blender for this one Since you only need a still image, there is no need for elaborate smoke simulations that take days to render.
If you really really wanted to use blender, try looking into Abstract Wave with Particle System
But really, it would be so much simpler, easier, and less time consuming to use something designed for creating art like this: http://www.escapemotions.com/products/flamepainter/
I even have made a demo of something similar to this that runs in realtime in JS to prove that you could code it yourself if you too. http://codepen.io/Thisisntme/full/KNpPEz/
If you wanted to know, my codepen works by creating a sequence of lines, and then dragging them down the screen (from left to right although it doesn't really matter) all while changing the y position with a few trig functions.