Mantle plumes arising from deep sources in the Earth are thought to have played a critical role in determining the planetary geodynamics. The plumes originate mostly from gravitational or thermochemical instabilities at the core-mantle boundary, triggered by density fluctuations due to thermal or chemical variations. Understanding the initiation mechanics of such instabilities is key to comprehending the formation of these deep-mantle plumes, reflected from hotspots scattered around the globe. Previous studies have explained their growth within a theoretical framework of Rayleigh-Taylor (RT) instabilities. However, a critical aspect that has been largely overlooked is the potential influence of layer-parallel global flows on the dynamics and initiation processes of instabilities. The present study combines 2D finite element particle-in-cell numerical simulations with a linear stability analysis to show the impact of global flows on the growth kinematics of RT instabilities in a thermal boundary layer at the core-mantle boundary. The simulation results indicate that the global flow acts as a counter factor to dampen their growth rates. At a threshold global flow velocity the dampening effects completely suppress the instabilities, allowing the entire system to advect in the horizontal direction. The stability analysis also predicts a non-linear increase in the instability wavelength with increasing global flow velocity. These new findings imply that the spatial frequency of plumes can drop remarkably in kinematically active regions of Earth's mantle. This study finally offers a possible explanation for unusually large spacing between major hotspots in the light of instability mechanics under global flows.