Don’t let it, if you want to keep that harvest coming. If you allow the plant to flower, it will tell itself, “I’ve fulfilled my life’s purpose by making seed, so I can just stop growing.” So check every day, and pinch the flowers as soon as they appear. In areas with a long growing season, you can refresh plants even more by trimming the tips and fertilizing with fish emulsion or Miracle-Gro® LiquaFeed® Tomato, Fruits & Vegetables Plant Food (follow label directions). Have more basil than you can use? Put a few sprigs in a small vase to perfume the kitchen.
With a little attention and care (and a lot of pinching!), your basil can continue to produce a nice harvest until cold weather arrives. Basil will turn brown at the first sign of frost. So when a freeze is in the forecast, consider harvesting the remaining leaves and making pesto, then freezing it for ready access to that fresh basil flavor.