I'm not sure how much winter hardiness varies for different leek varieties, but certainly worth a try to overwinter them, especially at young stage. You could try mulching them too, to increase the chances.
Also you can cut them back to about an inch from the ground, eat the tops and leave the stumps to regrow next season. So nothing at all would be lost from trying.
If they survive they will likely flower next season. Pearls form at the bottom of the flower stalks when they are done. If the flowers are late, I think you can cut them to hasten the pearl forming process.
The only drawback of American Flag, they flower quite late for our short season, so it is a challenge to collect much seed. There was some seed formed this year though, so I've cut the heads and am letting them finish/dry out in a paper bag. From past experience, this can take a long time! On my last try, the stems remained green for months. Seed was viable though, but mostly not ready until January, and I had to remove them manually from the capsules since they didn't open and scatter as they would if they finished and dried in the field. I'll let you know if I get some seed from this batch, I can send you some.
Seed viability for leeks and other alliums is usually quoted as only one year, although my fresh seeds here have remained viable for me the second year as well. So it is as well to use them up while they're fresh.
I have seeds of "Mammoth" leeks I intended to grow this year but my seed starting plans didn't pan out with the schedule for renos.
But I think they will still be viable and I'm determined to get them started this time. They are late, for sure, but I may try overwintering a patch all the same, and hope to keep them going from pearls if I cannot get seed.