I think there may be two different predators, and two different predation styles, in mind.The only situation I have seen where coloration may help is with visually oriented predators and where the chicken is trying hide. Hens incubating there clutch of eggs out in the open is the first situation where she covers the clutch moving very little with the exception of blinking her eyes. The way the feathers cover her body it is very difficult to see her breathing. The next is where a chicken freezes because is sees a predator although this approach does not work once the predator makes the chicken out. The final approach is where a chicken that is pursued by a predator flattens itself out in a depression or forces its way into vegetation. All these situations involve the bird becoming very still.
There are predators who are very alert to movement, but have very poor ability to distinguish colors. Against those, no amount of coloration is effective, because they are looking for change. They don't care what a thing looks like, only that the overall image is changing. Pattern *may* help, but not moving at all is FAR more effective.
The second is predators that hunt not based on movement, but on exception. We humans are that type of predator. Colors stand out, movement much less so. Against us and those like us, colors that blend in and patterns that break up the outline are very effective.
Against the first, we need birds of a certain behavior. Against the second, we need birds of a certain appearance.
Of course, its also possible i have fallen asleep to FAR too many nature shows. Rods and Cones, rods and cones.