Low arch or no arch, there are certain precautions you can take to lessen the risk of injury:
Buy appropriate running shoes (this alone can help keep you injury-free). The best shoes for flat-footed runners are motion-control or stability shoes with firm midsoles and features such as a medial post to reduce pronation. Do not wear shoes with lots of cushioning and little support; this allows too much pronation.
Avoid uneven running surfaces. Golf courses and trails may sound soothing to aching ankles and knees, but uneven ground can accentuate your pronation problem and make matters worse.
If your aches and pains persist despite these precautions, see a sports podiatrist.