In this study, we performed three dimensional viscoelastic flow simulations with freely suspended platelet particles for the application of effective coloring of polymers. The model problem with a partial drag surface mimics a recently proposed design to remove typical platelet particle orientation near the weld line. A standard combination for the particulate viscoelastic flow simulation techniques is employed: (i) the discrete viscous elastic stress splitting (DEVSS) scheme for the stable solution of the viscoelastic flow; (ii) the discontinuous Galerkin (DG) method to deal with the convection term in the viscoelastic stress evolution equation; (iii) a fictitious domain method (the rigid-shell description) for implicit treatment of the hydrodynamic interaction between particles and fluid. Through example problems with a single, two and many platelet particles, we report that the angular rotation of platelet particles is significantly reduced in a viscoelastic (Giesekus) fluid compared with that in a Newtonian fluid and that non-uniform angular rotation of particles can be generated by the spatial distribution of particles, which facilitates enhanced orientational dispersion by randomizing the platelet particle orientation.