We experimentally and theoretically investigate the photonic generation of microwave signals using a long-wavelength single-transverse-mode vertical-cavity surface-emitting laser (VCSEL) subject to two-frequency orthogonal optical injection. We study if a significant reduction of the linewidth is achieved in the double injection locking regime. In this regime, the VCSEL is subject to optical injection by two master lasers in such a way that stable locking is also observed if only light from one of the master lasers is injected. Our model includes the effect of the injected light reflected at the VCSEL's mirror generalizing previous modeling of reflection-mode optical injection-locked VCSELs. Our model also describes the high coherence associated to stable injection locking states and takes into account phase fluctuations in both master lasers. We observe no significant reduction of the linewidth in the double injection locking regime because the linewidth is mainly determined by the phase fluctuations of the two master lasers.