Cell-free massive MIMO and symbiotic radio are promising beyond 5G (B5G) networking architecture and transmission technology, respectively. This paper studies cell-free symbiotic radio systems, where a number of distributed access points (APs) cooperatively send primary information to a receiver, and simultaneously support the backscattering communication of the secondary backscatter device (BD). An efficient two-phase uplink-training based channel estimation method is proposed to estimate the direct-link channel and cascaded backscatter channel, and the achievable primary and secondary communication rates taking into account the channel estimation errors are derived. Furthermore, to achieve a flexible trade-off between the primary and secondary communication rates, we propose a low-complexity weighted-maximal-ratio transmission (weighted-MRT) beamforming scheme, which only requires local processing at each AP without having to exchange the estimated channel state information. Simulation results are provided to show the impact of the channel training lengths on the performance of the cell-free symbiotic radio systems.