We were fortunate enough to be the Flag Family on our last WDW trip. We are DVC members and were spending our 2nd WDW week at the WLV after a weekend at Vero Beach. Before heading to Vero we dropped off some luggage at the WL so we wouldn't have to drag it with us for the weekend. When we did that I stopped by Guest Services and asked about being the FF. I had my choice of 2 days the following week. When we checked in at the WL on Sunday and I stopped by Guest Services again to give them our room number I saw that the FF sheet was full for our entire stay. Needless to say I was glad I had asked when I did. Oh, and this visit was just 2 weeks after 9/11 when things were still slow.
I guess my point in relating this story is to tell you that yes, the FF program is very popular. Make sure you stop by as soon as you get to the WL. I think your length of stay will also be a big factor.
Oh, and to answer your other questions...the program is done just once each day, in the morning. When we did it in September we had instructions to be at Guest Services by 8:15am but I've heard that the time varies.
Good luck! It is a lot of fun!