This paper investigates the dynamic structure of the shock cone formed around a rotating hairy Horndeski black hole under Bondi-Hoyle-Lyttleton (BHL) accretion. The study examines the effects of the scalar hair parameter, black hole rotation, and asymptotic speed on the shock cone's formation and the trapped quasi-periodic oscillation (QPO) modes within it. Numerical simulations reveal that the scalar hair parameter significantly influences the shock cone's formation, with increasing absolute values of the hair parameter leading to the expulsion of matter away from the black hole horizon. The asymptotic speed also plays a crucial role, affecting the stagnation point and the rest-mass density of the matter within the shock cone. The deformation of the shock cone due to the scalar hair parameter can lead to changes or the complete disappearance of QPOs. The paper compares the numerical results with theoretical studies for $M87^*$ and GRS 1915+105 black holes, providing insights into the physical mechanisms underlying observed QPO frequencies.This paper investigates the dynamic structure of the shock cone formed around a rotating hairy Horndeski black hole under Bondi-Hoyle-Lyttleton (BHL) accretion. The study examines the effects of the scalar hair parameter, black hole rotation, and asymptotic speed on the shock cone's formation and the trapped quasi-periodic oscillation (QPO) modes within it. Numerical simulations reveal that the scalar hair parameter significantly influences the shock cone's formation, with increasing absolute values of the hair parameter leading to the expulsion of matter away from the black hole horizon. The asymptotic speed also plays a crucial role, affecting the stagnation point and the rest-mass density of the matter within the shock cone. The deformation of the shock cone due to the scalar hair parameter can lead to changes or the complete disappearance of QPOs. The paper compares the numerical results with theoretical studies for $M87^*$ and GRS 1915+105 black holes, providing insights into the physical mechanisms underlying observed QPO frequencies.