Just followed an excellent suggestion on the net: put one chicken in crockpot on top of onions, celery, etc. as standard. Cook chicken. After removing chicken from crockpot, pour off most of the broth, until there's just enough to cover the veggies. Then, hit that mess with the immersion blender. Salt & spice to taste, and hey, presto! Flour-free, no-wierd-gums-or-starches, gravy!
...update. Works great when served hot; add more salt & seasonings first. Does not work for frozen & reheated meals; the solids separate out from the liquid.