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Back and Forth

With the Feather Controller still selected, under the Key Controls window select Multi Layer from Layers Options under the Animation dropdown (fig 5).

Fig 5.

Change the current layer by selecting Layer 1 from the layer flap inside the FCurves tab. Right click on it to rename the layer FeatherFwdBkw (fig 6).

Fig 6.

Notice how there are no key frames on this new layer.
When working with layers it is a good idea to set place-holder keys on the main points of the animation. In order to do this, set a key frame by hitting the K key on frames 1, 10, 20, 30, 40, 50 and 55.
Go to frame 10 and translate the Feather Controller on the X axis towards the left of the screen by hitting the T key. Translate the controller roughly to 128 on X, you can eye ball it or you can type the number besides the field or the X axis on the bottom right corner of the viewer window (fig 7).  Set a key for this new position by pressing the K key.

Fig 7.

Key the Feather Controller on frame 20 at position 141, on frame 30 at -12, on frame 40 at -51 and on frame 55 at -217. The translate X curve should look like this (Fig 8).

Fig8.

Turn on the trajectories button in the top right side of the Viewer window, the new path for the feather shows up as a yellow curve (Fig 9).

Fig 9.

Feather Yaw

Create a new layer by pressing the New button on the Layer section of the FCurves tab. Rename the new layer FeatherYaw. Layers can also be created and managed through the Key Controls window (fig 10).

Fig 10.

Block the main parts of the animation by hitting the K key on frames 1, 10, 20, 30, 40, 50 and 55.
Go back to frame 10 rotate the Feather Controller on the Z axis -12 degrees by pressing the R key and then typing the value on the field. Set a key frame. 
Repeat the process by setting keys on that same axis on frame 20 at 21 degrees, frame 30 at -10 degrees and frame 40 at 17 degrees. The rotate Z curve of layer FeatherYaw should look like this (fig 11).

Fig 11.