If you wish to photograph the conventional and common shape of the flame, make sure that there are no air drafts around the flame. For this, a closed small room with darkness would be appropriate. In such a case, it would be advisable to use a camera setting around 1/6th of a second at f/8 to get a certain depth of field.
In case you are using a tripod, then you may use a high ISO setting with a fast shutter speed. This will capture the steady flame exactly as it is. Use ISO settings, 1600 or higher. This makes your photographs of flames look crisp.
If you are using a firm support for the camera, you may try a low ISO setting and a relatively slower shutter speed. Often, this option is useful if you don't have a tripod or want to use a compact camera.
Once you acquire the skills of photographing fire, you will be able to take very striking snaps of candle flames, other wick flames like those of oil lamps, birthday cakes, fire etc. To take great pictures of flames, you must be patient and spend plenty of time for practicing the skill. Play with the camera settings to get some interesting flame shapes.