In this study, the effect of a coflow of oxygen enriched air on the flickering of methane laminar diffusion flame is investigated using two visualization methods. Characteristics of the flame and instabilities of the shear layer between the hot combustion products and ambient air are extracted from flame images at various oxidizer flow rates and oxygen enrichments. These data are linked to the origins of the flame tip oscillations and to the presence or not of a detachment of the top of the flame. We observed that, when the flame is lifted, bulk flickering is always present because the flame remains in the zone of instabilities development. However, an increase of the oxygen enrichment decreases the flame length and the lift height and the instabilities observed in the external shear layer are pushed downstream modifying the behavior of the flame oscillation. Above a given oxygen content, the flame oscillations are observed to disappear.