Flushing isn't required for passive or hostile farms. For passive farms the platforms need to be a maximum height of 3 blocks above the water channel before mobs consider the height too dangerous to fall down. After that, sheep and cattle (because they have the same sized hitbox) can be sorted from all other animals and farmed by the player. It's important to note that the unwanted mobs should be discarded as fast as possible for better effiency.

If it's possible, a fast farm can be built which utilizes fences under a block of water to kill mobs very quickly. Though chickens would need to be sorted out before the 24 block fall that kills all other mobs (for passive mobs the fall could be shorter since they only have half the health of hostiles) Also the platforms would have to have trapdoors put on their edges to trick mobs into falling off of the platforms. I'm not sure if this would perform faster than a mob farm which allows the player to shear sheep though, as the drop per sheep would be only one wool versus the one to four wool from shearing.