The answer to 'why is my supply line won't flush' is that the supply line may be clogged or obstructed. This can happen due to buildup of mineral deposits, debris, or corrosion inside the pipe over time. Symptoms may include slow or incomplete flushing, gurgling noises, or water backing up.
To fix this, you'll first want to try clearing the clog by flushing the line with a plumber's snake or auger. This can often dislodge the blockage and restore normal flushing. However, if the problem persists or the clog is difficult to reach, it's best to call a professional plumber. They have the specialized tools and expertise to fully inspect the supply line, identify the root cause, and make any necessary repairs or replacements.