I haven't tried leeks, but I've done other alliums, including chives.

The trick is to pick early, when the individual flowers are just staring to open or even just before then, when they're still bunched together. Alliums keep on opening after they're picked and can go past their best point.

I air-dry chives and other alliums by hanging upside down. You may find that the stem takes a long time to get truly dry. Good luck, and come back in a month or so to tell us how it went. I agree that leek flowers are beautiful and would like to try some myself sometime.