Create a new timeline to animate the butterfly and flapping wings and set an action keyframe for it to loop or ping-pong.
Go to the main timeline, select the butterfly and move it to its start point. set keyframes for the left and right originl positions, then click on the bezier symbol next to the origin (left) keyframe button. This will set it as a motion path. Click on the record button, move the time cursor to the exit time, then drag the butterfly to that position. Turn off the recording.
To create the irregular flight path, double click anywhere along the motion path to create a bezier point and adjust as desired, then add more beziers and adjust. You can also drag the bezier points along the timeline to have the motion speed up and slow down as desired. Note that you can set the butterfly to follow the angle of the path or to retain a fixed orientation.