In this paper, we study the downlink (DL) spectral efficiency (SE) of a cell-free massive multiple-input-multiple-output (MIMO) system with Rician fading channels. The phase of the line-of-sight (LoS) path is modeled as a uniformly distributed random variable to take the phase-shifts due to mobility and phase noise into account. Considering the availability of prior information at the access points (APs), the phase-aware minimum mean square error (MMSE) and non-aware linear MMSE (LMMSE) estimators are derived. The MMSE estimator requires perfectly estimated phase knowledge whereas the LMMSE is derived without it. Besides, two different transmission modes are studied: coherent and non-coherent. Closed-form DL SE expressions for both coherent and non-coherent transmission with maximum-ratio (MR) precoding are derived for the two estimators. Numerical results show that the performance loss due to the lack of phase information is small and coherent transmission mode performs much better than non-coherent transmission.