This paper investigates mobile video delivery in a heterogeneous wireless network from a video server to a multi-homed client. Joint source-channel coding (JSCC) has proven to be an effective solution for video transmission over bandwidth-limited, error-prone wireless networks. However, one major problem with the existing JSCC approaches is that they consider the network between the server and the client as a single transport link. The situation becomes more complicated in the context of multiple available links because involving a low-bandwidth, highly lossy, or long-delay wireless network in the transmission will only degrade the video quality. To address the critical problem, we propose a novel flow rate allocation-based JSCC (FRA-JSCC) approach that includes three key phases: (1) forward error correction redundancy estimation under loss requirement, (2) source rate adaption under delay constraint, and (3) dynamic rate allocation to minimize end-to-end video distortion. We present a mathematical formulation of JSCC to optimize video quality over multiple wireless channels and provide comprehensive analysis for channel distortion. We evaluate the performance of FRA-JSCC through emulations in Exata and compare it with the existing schemes. Experimental results show that FRA-JSCC outperforms the competing models in improving the video peak signal-to-noise ratio as well as in reducing the end-to-end delay.