In air assisted atomization, small droplets arise from the stripping of a liquid jet (or a film) by a fast gas stream (Lasheras & Hopfinger 2000, Eggers & Villermaux 2008). Yet, the incoming liquid jet is seemingly never fully atomized by the stripping process alone. Instead, the remaining jet experiences a flapping instability, similar to the instability observed on liquid sheet configurations: the resulting large scale structures break into large liquid lumps some distance downstream the injection. Little is known on the underlying mechanism of this instability and on the characteristics of the large drops it produces, though these large drops probably control flame extent in combustion devices. We suggest in the present study that this instability could be triggered by non-axisymmetric Kelvin-Helmholtz modes. Indeed, in coaxial injector configuration, non-axisymmetric modes of the KH instability can be observed. First, we study the dependence of KH modes upon two control parameters, namely the liquid and gas velocities, and discuss the symmetry of these modes. Secondly, we investigate a possible link between non-symmetric modes of KH instability and the large scale instability. Finally, amplitude of the large scale oscillation is measured as a function of gas and liquid velocity.