Passive metal reflectors for communication enhancement have appealing advantages such as ultra low cost, zero energy expenditure, maintenance-free operation, long life span, and full compatibility with legacy wireless systems. To unleash the full potential of passive reflectors for wireless communications, this paper proposes a new passive reflector architecture, termed flexible reflector (FR), for enabling the flexible adjustment of beamforming direction via the FR placement and rotation optimization. We consider the multi-FR aided area coverage enhancement and aim to maximize the minimum expected receive power over all locations within the target coverage area, by jointly optimizing the placement positions and rotation angles of multiple FRs. To gain useful insights, the special case of movable reflector (MR) with fixed rotation is first studied to maximize the expected receive power at a target location, where the optimal single-MR placement positions for electrically large and small reflectors are derived in closed-form, respectively. It is shown that the reflector should be placed at the specular reflection point for electrically large reflector. While for area coverage enhancement, the optimal placement is obtained for the single-MR case and a sequential placement algorithm is proposed for the multi-MR case. Moreover, for the general case of FR, joint placement and rotation design is considered for the single-/multi-FR aided coverage enhancement, respectively. Numerical results are presented which demonstrate significant performance gains of FRs over various benchmark schemes under different practical setups in terms of receive power enhancement.