What is the best thickening agent to use in poultry gravies if one cannot use AP flour? I am making our turkey gravy gluten-free this year. Thanks.

You could use cornstarch. It generally only requires half as much cornstarch as you would use flour. Mix it with a little cold water or cool broth, and whisk it in just before the gravy comes to a boil. It will thicken up fairly quickly, and doesn't need to be cooked as long as flour to remove the "uncooked starch" taste. If you don't like the idea of cornstarch, you can also use arrowroot, tapioca, or potato starch/flour as well. Personally I prefer cornstarch, but any of them will do the job. If you like a splash of cream in your gravy though, don't use the arrowroot because it can make the results slimy.