The flame-intrinsic Kelvin−Helmholtz (KH) instability, a self-oscillation of laminar flame fronts extending to the streamwise direction, was experimentally investigated using inverted conical premixed flames, and the governing parameters of flame flickering were deduced. We supposed that the flame flickering is caused by the KH instability, and the feature may be determined by which is dominant between the buoyancy-driven one taking place in the shear layer between hot products and ambient air and the flame-intrinsic destabilization because of the vorticity generation of flame fronts. For the distinction between the two, the former effect was excluded using a cylindrical quartz tube preventing the interaction with the ambient air and the latter was characterized by the flickering frequencies and wavelengths obtained by chemiluminescence signals and instantaneous images, respectively. Besides, laminar burning velocities were measured from the velocity normal to the flame front by the particle image velocimetry (PIV) method. From the dimensional analysis and physical considerations on an oblique plane flame front, it was estimated that the frequency will be determined by the flame structure and described by the modified Richardson number Ri_f involved with the flame thickness and laminar burning velocity. From the experiments, it was revealed that the Strouhal number, dimensionless frequency, is proportional to Ri_f^0.869 rather than the conventional Richardson number within the experimental conditions. This means that the flickering motions could be influenced by the flame-intrinsic KH instability described by the flame structure, in addition to the buoyancy-driven KH instability determined by the mixture velocity and length scale of burner geometry.