Low frequency noise close to the carrier remains little explored in spin torque nano oscillators. However, it is crucial to investigate as it limits the oscillators frequency stability. This work addresses the low offset frequency flicker noise of a TMR-based spin-torque vortex oscillator in the regime of large amplitude steady oscillations. We first phenomenologically expand the nonlinear auto-oscillator theory aiming to reveal the properties of this noise. We then present a thorough experimental study of the oscillators $1/f$ flicker noise and discuss the results based on the theoretical predictions. Hereby, we connect the oscillators nonlinear dynamics with the concept of flicker noise and furthermore refer to the influence of a standard $1/f$ noise description based on the Hooge formula, taking into account the non-constant magnetic oscillation volume, which contributes to the magnetoresistance.
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