We investigate the coupled behaviour of two oscillatory flames produced by separate bundles of candles, referred to as candle-flame oscillators, as the distance between them is varied. Each bundle consists of four candles whose individual flames are fused so that the resultant flame produces self-sustained limit cycle oscillations. The recent study by Manoj et al. [Scientific Reports 8, 11626 (2018)] has reported the occurrence of four different modes of coupled behaviour, which include in-phase synchronization, amplitude death, anti-phase synchronization, and desynchronization by observing the flame dynamics of such coupled candle-flame oscillators. Here, we investigate the physical mechanism behind the occurrence of these different dynamical modes. Towards this purpose, we perform simultaneous measurements of the flow field around the candle flames using high-speed shadowgraph and of the reaction zone of each flame using high-speed CH ∗ chemiluminescence imaging. We notice that these modes are distinguished by the distinct features of the flame dynamics and the corresponding buoyancy-induced flows surrounding the flames. We observe that the difference in the interaction of vortices, formed due to the instability of buoyancy-induced flows around each flame at various distances, plays a significant role in inducing different modes of coupled dynamics between the oscillators. Furthermore, we find that the change in the length scales of vortices shed around the flames is a contributing factor in increasing the frequency of the oscillators during the transition from in-phase to anti-phase mode of synchronization. © 2019 Author(s).