Dragging the shutter is a cool technique that professional photographers use when shooting pictures in a room and they want to include some of the ambient lighting in the picture.
In the first photo, the speed was set at 15 seconds (obviously I used a tripod) to capture the glowing flame. However, you see little else of the scene.
In the second picture, I used a flash, and the camera speed was set at 1/60 second. You can see the scene, but the glow of the candle is lost.
In the final picture, the camera speed was set at 15 seconds (like in the first shot) and I used the flash. This time, you can see the setting and the pumpkin, but the glowing effect of the candle is still there. It doesn’t look like the wind extinguished the flame. A much better picture than the other two.
Try it out for yourself, and experiment with all kinds of possibilities. The key is to set the speed according to the ambient light and let the flash add whatever else is needed.