It takes approximately 20 months to go from seed to seed. And you should have about 15 plants to save the seeds from to ensure adequate pollination. Each of the 100s of flowers will produce 2-3 seeds so that each plant will have hundreds of seeds. If your leek has a second flower head near the base of the plant, remove and discard it.
The seeds are covered in a thin green seed coat and this changes color as the seeds mature. When trying to determine when to take the flower head from the stem, sample a few of the seed pods from around the flower head to see if there are any black seeds present. If they are present, you can remove the whole flower head. As the seed pods age, they become more papery white and you can see the black seeds inside. But if you leave them too long on the stem, you can lose them to the weather as they open and fall to the ground.
When you remove the flower head, place it upside down in a cardboard box, allowing some space for ventilation. Leave the seeds to dry and mature over winter in a warm room, eg. 15 deg C, and the seed pods will open up dropping the seeds into your box ready for spring planting.
To plant from seed, sow indoors 8-10 weeks before the last expected spring frost. Plant seeds 1/2 inch deep in pots at least 6 inches deep, thinning to 1 inch apart when the seedlings are 3 inches tall. Transplant when seedlings are hardened and the ground can be worked.