Flames are associated with heat and speed, and thus, automobiles and sports. Most people paint flames for decorative purposes--such as in the case of decals and logos. Flames are not complicated. With a little practice, they are easy to paint.
Preparation
Choose your colors. Red, orange and yellow are the most common. Select the medium in which you will be working (oil? acrylic?) and the surface on which you will be painting. Before you begin painting, study examples of flames that people have made. Examples can be found online, on motorcycles, trucks, shirts, helmets and bumper stickers.
Drawing
Draw the outline of the flames with a pencil before beginning to paint. Flames will be built in layers. Like an onion, each new layer mimics the layer inside it. Colors most often go from light to dark as the layers build from the inside out. Draw the inner-most layer. Curve the flames moderately. Flames will not reach around objects or delineations in the surface on which you are painting. Flames grow in a line. They will be thickest at the base and taper until they end in a point. Draw a layer outside the interior layer. Draw a third layer outside the second layer.
Painting
Paint the interior layer the lightest color and the outer layer the darkest color. The middle layer will be an intermediate color between the extremes of light and dark.
Alternatives
One variation of this style is to blend the layers together so that they are not detectable as separate layers. Another variation is to invert the color order, so that the colors go from darker to lighter. You may also try to make each layer different from the layer inside of it. Flames may also be painted in colors other than red, orange and yellow. Flames are often identified by their distinctive shape. They may still be recognizable as flames even if they are painted in shades of blues, purples and greens.