I sewed up a skirt out of green dupioni silk with a cotton lining. Along the hem, I applied sections of Adafruit NeoPixel Strips cut to a variety of lengths, arranged vertically. I used 6 meters worth of strips all told, totalling 358 individual LEDs. Over the strips I couched down layers of polyester batting and cotton muslin to diffuse the light, since I wanted the final effect to be more glowy than sparkly. This also had the effect of attaching the strips securely to the skirt. Over the diffusion layers, I appliqued flame shapes made out of a wide selection of fabrics in reds, oranges, and yellows.
The pixel strips are chained together and controlled by an Adafruit Feather M0 Bluefruit LE microcontroller board and powered with a 2.1A USB battery pack in one pocket. The software running on the Feather flickers the bottom three LEDs in each strip randomly in red and orange to simulate embers, and animates the rest of the strip to give the effect of flames and sparks rising upward.
Here are some pictures of the skirt:
Here is a video that shows this in action: