Integrating microscale liquid crystal polymer flakes into host materials takes advantage of their compact shape and heightened responsiveness to electric fields, facilitating a range of switching capabilities and related applications, such as smart windows and E-paper displays. However, the complex physics controlling the movement of these flakes within liquid crystal hosts remains partly mysterious. This paper aims to elucidate the underlying physics that governs the behavior of nematic liquid crystal polymer flakes within nematic liquid crystal hosts. The uniaxial flakes are introduced into nematic liquid crystal hosts, which have positive or negative dielectric anisotropies. They are then arranged in devices with various alignment layers: parallel, perpendicular, or twisted. We compare and analyze the rotation and relaxation times of these flakes, observing their behaviors at specific moments to identify the factors influencing their motions. Our research pinpoints three primary factors that impact the movement of these flakes: anchoring, elastic, and interfacial polarization effects. Moreover, elastic and anchoring effects play more prominent roles and contribute earlier than the interface polarization effect in the liquid crystalline hosts upon the application of electric fields; flakes can relax back to their initial state with the help of the anchoring effect. This comprehensive understanding not only contributes to the fundamental study of flake dynamics but also paves the way for enhanced performance and broader practical applications, particularly in photoelectric fields, such as fast-switching smart windows.