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Wow, thanks so much for the speedy responses (and so many of them.) below is the jist of what I received...Happy Thanksgiving!!

Corn starch does not work well.  The best flour to use is sweet rice flour

I used 3 bean flour from Bette Hagman's cookbooks and found that worked very well

Cornstarch works great--just follow the instructions on the box.  I use Swansons chicken broth.  The 14 oz cans both fat free and 99% fat free are GF

I prefer Sylvan Border all purpose flour mix to thicken gravy rather than cornstarch

I use arrowroot--McCormick's sells it in a spice bottle. It is more expensive than cornstarch--but you use much less. I find it less likely to lump

I use Mochiko, aka sweet rice flour. I avoided it for years thinking it actually was a "sweet" tasting flour, finally tried it one day and found it worked better than anything else I had tried. However, if you have leftover gravy that you save for the next day, you will have to thicken it with more sweet rice flour the next day. It tends to get watery after you save it in the refrigerator. I have no clue why. I use it all the time to make green chile gravy for enchiladas. I saute tomatoes, onions, and green chile, add water with sweet rice flour in it, then add hamburger meat once it has reached the desired thickening stage. That becomes my sauce for green chile enchiladas. I'm from Albuq. New Mexico, so green chile enchiladas may not be a dish you desire to eat

 think potato starch or potato starch flour works the best

tapioca starch flour

I use 1/2 corn starch & 1/2 rice flour

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