In this work, we focus on the tumbling dynamics of rod-like and semi-flexible polymers in mixed flows, which vary from simple shear to pure rotation. By employing a bead-rod model, the tumbling pathways and periods are examined with a focus on the angular distribution of their orientation. Under the mixed flows, the tumbling dynamics agreed well with earlier studies and confirmed the predicted scaling laws. We found that the angular distribution deviates from that of shear flow as the flow type approaches pure rotation. Finally, we investigated the angular distribution of $lambda$-DNA in a shear flow and found that the present numerical simulations were in quantitative agreement with the previous experimental data.