I was just starting a barbecue fire by blowing on the smouldering coals when I realised I had no idea what the sound was actually caused by. I can make the sound by blowing at almost any flame I can think of, and I guess it is perhaps related to the increased oxygen consumption and a turbulent flow. Why does a disturbed flame make a sound?
The roar is indeed due to turbulence.
When a solid (or liquid) burns it isn't the solid that burns. The heat causes the solid to vaporise or emit vapour and it's the vapour that burns. When you have a steady flame the vapour burns smoothly. However, when you blow on it you make the vapour flow, and therefore the flame, turbulent. Under these circumstances the vapour burns as, in effect, a series of tiny explosions and this causes the roar.
I couldn't find a basic article on this subject (for once Wikipedia let me down), but if you Google for "flame turbulence sound" you'll find lots of scientific papers on the subject.