When I eat chicken and dumplings I like to eat cornbread or fried okra which goes great with chicken and dumplings.
My Grandma used to make homemade chicken and dumplings and she would serve both cornbread and some fried okra along with the chicken and dumplings.
The chicken meat was always fresh and she grew the okra and raised the chickens that she made the chicken and dumplings from.
That was some good tasting chicken and dumplings and she would give us some cornbread and okra with it that was fried okra and the cornbread was homemade as well.
Some other things that go good with chicken and dumplings are, Brussels Sprouts, Fresh Green Salad, Green Beans, Fried Okra, Grape Salad, Fried Apples and Corn Pudding.