A single candle flame draws in air at the sides while the hot gases that are produced rise quickly above it. This is convection. When two flames are close together the convection current is changed in shape and the air does not come from all sides equally. Effectively, the flames in your candles appear to be trying to join up.

In huge fires these convection currents can become very powerful so that a strong wind blows in from all sides and the flames steeple up to great height in the middle. I think this was what happened in Dresden