Well, I don' t know how " easy" it is to learn. For me, it was sure a lot easier to learn than gobbling. I prefer to use a mouth call as it leaves my hands free to use the hat-trick mentioned above. The fly down cackle can also be done easily enough on a box call.

Let' s start with the call itself... I begin by making a couple soft clucks. Then I go into the cackle. A fly down cackle will " burst out" and " step down" as it reaches the end. In other words, you will want to start the call out rapidly and gradually slow in pace to simulate a hen approaching the ground.

With the mouth call... Use your jaw! Don' t try to burst out all of those fast clucks while concentrating on your tongue. Your jaw can usually move more rapidly than your tongue and you will have less chance of " tripping up" when using your jaw. Just focus on dropping your jaw rapidly. This will take your tongue where it needs to be automatically.
Here' s a recording from one of my sites... Fly-Down-Cackle

With a box call... I find it is best to use the back side rail (left rail if you are right handed). Just rotate the box call around and hold it similar to the way you hold a boat paddle call. Another method (my prefered method) is to hold the call with the pivot screw pointing toward you and the handle facing away from you. Again, start out making a few clucks and then " pop" the paddle of the call against the rail rapidly. Remember to step the call down in volume and pace as you go.
Here' s a video clip from another one of my sites... Fly-Down-Cackle Video