If the flies are fruit flies usually on indoor potted plants then cover the soil with a mulch of marbles, corks or gravel to keep the insects from laying eggs in the soil. You can fill a white saucer up with water and attract the flies with lemon scented dishwashing soap. The flies will fall into the water drawn by the lemon scent and drown. If the flies are outdoors a mulch of wood chips may help but they could be flea beetles, gnats or some other pests. Perhaps if you sent an image of a dead fly I could be of more help. The good news you should still be able to harvest and use the basil so happy pesto to you! Keep growing, Marianne Binetti