Silkies cannot fly. I'm not aware of any others that cannot fly. Even the big bulky ones (not Cornish X, more Jersey Giant/Brahma) can fly quite well when younger and some older ones will sometimes surprise you.
It's not so much "can" they fly but whether they "want to". They generally don't want to fly somewhere they can't see. With a solid wooden fence it's unlikely they will want to fly over it, but they like to perch. It's quite possible they will fly to the top just because it's fun to perch there. Who knows which side they might hop down on?
If you make the top look like it is not a good place to perch they will not want to fly up there. If you take some mesh wire like chicken wire, hardware cloth, or welded wire and attach it vertically to the top of your fence so it sticks up 6" or a foot, they will not want to fly up there. They can't land. so take a strip of wire 24" thick, attach it to the top of your wooden fence and again about a foot down and the stiffness should cause it to stand. I don't think it looks that bad either.
But then, do you have trees there with limbs good for perching?