Waving a dead chicken is a slang expression for an effort to solve a problem even when the effort is expected to be futile. The problem-solving effort may be a sincere though desperate effort or it may be "for show" to demonstrate to superiors that everything has been tried.
Consider the example of a computer application that does not properly run because the computer's operating system does not support that application. The department head demands that the application be made to run, but is unwilling to change operating systems. So the technician waves a dead chicken by trying all sorts of tricks known to be futile, but that make the department head think an effort is being put forth. The antivirus program is shut down, the firewall is disabled, the application program is installed with different folder names, and still the application does not work. The hope is that if the dead chicken is waved long enough, the department head will eventually start to believe that the technician might be correct. (At this point, the technician might install the application in a computer with a different operating system to show that it will run properly there.)