It is best not to allow the chives to
flower. Unless you just like the
flowers, because once the chives
flower, the leaves will be tough.
Also, when you do that and they reseed and new
plants are generally inferior to the original
plant.
What I have done many times, is just to keep snipping and using the chives, they will keep
growing. Dig them up and bring them in when the weather gets cold.
If you don't want to do that, you could try just chopping them completely down before they
flower. I have had some that came back that way too.