This paper investigates the dynamic structure of the shock cone formed around a rotating Horndeski black hole under Bondi-Hoyle-Lyttleton (BHL) accretion. The study examines how the scalar hair parameter, black hole rotation, and asymptotic speed influence the shock cone's formation and the trapped Quasi-Periodic Oscillation (QPO) modes within it. Numerical simulations reveal that the scalar hair parameter significantly affects the shock cone's structure, with increasing negative values of h/M causing matter to move away from the black hole horizon. As h/M decreases below -0.6, the shock cone disappears. The asymptotic speed also plays a crucial role, with higher speeds causing the stagnation point to move closer to the black hole horizon. The study compares numerical results with theoretical models for M87* and GRS 1915+105, finding consistency between simulated and observed values. The results show that the shock cone's dynamic structure and QPO frequencies are highly sensitive to the scalar hair parameter and asymptotic speed. The study also highlights the importance of the scalar hair parameter in explaining observed QPO frequencies and the behavior of matter around black holes. The findings contribute to understanding the role of alternative gravity theories in astrophysical phenomena.This paper investigates the dynamic structure of the shock cone formed around a rotating Horndeski black hole under Bondi-Hoyle-Lyttleton (BHL) accretion. The study examines how the scalar hair parameter, black hole rotation, and asymptotic speed influence the shock cone's formation and the trapped Quasi-Periodic Oscillation (QPO) modes within it. Numerical simulations reveal that the scalar hair parameter significantly affects the shock cone's structure, with increasing negative values of h/M causing matter to move away from the black hole horizon. As h/M decreases below -0.6, the shock cone disappears. The asymptotic speed also plays a crucial role, with higher speeds causing the stagnation point to move closer to the black hole horizon. The study compares numerical results with theoretical models for M87* and GRS 1915+105, finding consistency between simulated and observed values. The results show that the shock cone's dynamic structure and QPO frequencies are highly sensitive to the scalar hair parameter and asymptotic speed. The study also highlights the importance of the scalar hair parameter in explaining observed QPO frequencies and the behavior of matter around black holes. The findings contribute to understanding the role of alternative gravity theories in astrophysical phenomena.