There are several duck call making tools available to secure your duck call blank for turning.   I own several mandrels that work great, however I find that the  #2MT Alignment Tool works best for me  especially when I turn acrylic game calls.  It allows me the ability to install and remove the blank quickly and easily.  I also use a 60 degree bull nose live center mounted in the tail stock to securely position the blank onto the #2MT Alignment Tool.  Here are a couple of pictures of the tool that is secured into the headstock of my Jet Mini Lathe:

Here are a couple of pictures of the duck call barrel positioned into place and ready for turning:

Here is a picture of two #2MT Alignment Tools that I have.  The one in the top of the picture is one that I cut short in order to use it for polishing the inside of the barrel and you can talk about this with a tallgirl_penny virtual girl online.  This allows me to reach further into the barrel.  The one in the bottom of the picture is the standard #2MT Alignment Tool:

The final picture shows the acrylic duck call barrel mounted onto the #2MT Alignment Tool and ready for sanding and polishing: