Ours is just plywood— 2x6 sounds fine.
My coop door is only 2 feet off of the ground. Most of the time however they don't even walk up the runway, just jump. You could either make a really long walk plank up to the door from the ground, or make a shorter one that connects to a cinder block a foot or two off of the ground that they can jump on. Just how I double (or triple) step going up stairs, I noticed that my chickens jump directly into the door.
There is no angle that is minimum. If it is kind of steep, you could put little slats or rows of plywood on the ramp so they have traction.
Trial and error! You may see that your chickens don't even need the ramp. I've seen chickens fly up 4 feet, but a ramp is nice.