1- Open a new Document(700*300px) Fill the background with black color.

2-Make a new Layer.(Ctrl+shifr+N)  Using Rectangular Marquee tool, Fill about 1/4 th part in the bottom with white color.

3-Apply Gaussian Blur (around 12px)

4-Duplicate this layer 4 times. Use Ctrl + J (total 4 blured layers)

5-Among this 5 layers, Select one and hide 4 other layers. We are starting work in this layer.

Now select the smudge tool. Make strength 70%

Make Flames with smudge tools as shown. Use Different Brush sizes(less than 50 px) to make the flames.

6-Repeat same in other 4 layers.

7-Now the animation part starts. Open Animation palette : Window>animation

8-Male four frames By clicking in the new frame button.

9-Select Each frame and make only 1 layer each visible in each frame.

10-Click on the Play button in the animation Pallet to see the effect.

11- Adjust color balance.

Midtones:
+60 0 -15
Shadows:
+100 0 -30
Highlights:
+50 0 -30

12- select File>Save for Web and Devices.
Save as GIF

PSD