They will stay tender enough to eat, as a rule, until the flower stalk grows to about double the height of the foliage and the blossom bud gets about the size of a large marble/ping pong ball. You can eat the "scape" -- the bud and stalk, if you wish, much in the way garlic scapes are eaten.

After that, it will to too tough to really eat, although you could always throw it into soup, etc., and remove and discard after it releases its flavor into the broth much like one would with bay leaves.

The flower is very attractive and ornamental. After flowering, it makes a large round green seed head which self-sows easily, and 2 to 4 baby leeks will emerge in the fall from the base of the old flower stalk to repeat the whole cycle.

Great info denninmi -- thanks! I left a few of my leeks in this year to flower, because I heard they are very pretty and that the bees love them. So glad to know they will make more leeks for me for next year, too.

Really? Leeks(never grown them) are perennial or biannual.
Thanks for the tip.

Thanks denninmi. I believe I'll leave some of them in place to form those baby leeks around the base. Sounds like I could have a perennial leek bed.