This paper considers a cooperative simultaneous wireless information and power transfer (SWIPT) network with a source-destination pair and two full-duplex (FD) relays, where the two relays are powered by radio frequency signals from the source and forward the source messages to the destination. The amply-and-forward (AF) relaying protocol is studied. Specifically, we characterize the performance of the AF relaying protocol, and the outage probability is analyzed with a close-form expression. In addition, to avoid a zero diversity gain, a dynamic hybrid relaying scheme that switches between full-duplex and half-duplex relaying is applied to the FD relaying scenario. The impact of the hybrid relaying scheme is characterized via the analysis of the outage probability. An exact expression of the outage probability is provided, and its approximation is also analyzed. Such an approximation is shown to be accurate at high signal-to-noise ratio (SNR).