The answer to 'backflow preventer won't flush' is that a backflow preventer that won't flush is often caused by a clogged or malfunctioning relief valve. This can happen due to mineral buildup, debris, or wear and tear over time. Symptoms include the preventer not draining properly after use and potential backflow issues.
To troubleshoot, you can try flushing the relief valve by shutting off the water supply, opening the test cock, and allowing the water to drain out. If that doesn't work, you may need to replace the relief valve or the entire backflow preventer. This is generally a job for a professional plumber, as backflow preventers require specialized knowledge and tools to service properly.