Complex flows or vortical structures are observed around flapping wings. In particular, as observed in various experiments and numerical simulations, these flows are affected when kinematic parameters and translational velocity functions are changed. In the present study, numerical simulations of three-dimensional flows around a flapping wing are conducted to investigate parameters and translational velocity functions on the stroke reversal stage using immersed boundary lattice Boltzmann method. We consider a flapping Drosophila wing without pitching motion, and the effects of the stroke amplitude and stroke reversal duration are investigated. First, at high stroke amplitude, we found that a hairpin-like vortex loop is obviously observed. Second, the stroke reversal duration affects remnant vortex structures in the wake. In addition, this parameter affects a time instant which the wake capture occurs. Third, it is shown that the translational velocity function has a significant effect on drag force. If the translational velocity function is modeled with trigonometric function, the drag force has a discrepancy with well-known experimental data. In order to solve the problem, we suggest a higher order polynomial. As a result, our function shows a better agreement with the experimental data.