Flexible Raids will be queued for like heroic scenarios -- players will form a pre-made group, then join the queue. The raid will be cut up into sections, just like in the Raid Finder, so you will be queueing for, say, a set of three bosses. If everyone in your pre-made group has already killed boss one and boss two, the bosses and their trash will simply not be there. You will wander through straight to boss three and start from their trash. However, if even one player in your group has not killed boss one and boss two, they and their trash will be there. In order to progress to boss three, you will have to kill boss one and boss two.
But, fear not. Because on repeat kills of bosses, while, just like in the Raid Finder, you will not be eligible for loot, there are other incentives. Firstly, trash drops loot, just as Taepsilum mentions, but secondly, repeated bosses still award valor. Valor is dropped from Flexible raids on a boss-by-boss basis, and repeating bosses will still give you points. What's more, players can use their bonus rolls on repeat bosses to get greater chances of loot.
What's your take on this? It seems like a great system, gives player an incentive to do the raids more than once a week if need be to help friends and make finding groups an easier task. However, attempting to look at this from the angle of progression-focused hardcore guilds, it seems possible that this could be used creatively to spam a single boss or wing over and over for specific drops. Nonetheless, in the grand scheme of things, that's a small price to pay!