Recently, it has been shown in the literature that in a relaying network utilizing multiple relay precoding techniques, the signal-to-noise ratio (SNR) at each destination node will scale linearly with the number of relays K, which is referred to as the distributed array gain (DAG) K. In this paper, we focus on the performance of multiple relay precoding based on limited channel state information (CSI) feedback, which is different from the prior studies that assume perfect CSI at each of the relay nodes. Our analysis shows that the conventional limited feedback scheme fails to obtain the DAG K, which is a consequence of the phase ambiguity introduced by the channel quantization function. Based on the theoretical analysis, we propose a novel feedback and precoding procedure, and prove that the proposed procedure can obtain the DAG K with only one additional feedback bit for quantizing each relay-destination channel compared with the conventional scheme. Simulation results verify that with the proposed procedure, the SNR performance is effectively improved when the number of relays K is small, and scales linearly with K in relatively large K regime.