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1) An animal's immune system plays a roll in worm infestation and will fend it off to some degree. However, in nature, animals are not routinely penned up and exposed to the high concentrations of worm eggs/segments/etc. like they often are when kept by people; in the wild they roam when/where they want. Animals with weaker immune systems and/or higher level exposures will likely die if left to their own devices. Also, keep in mind that parasites are often species specific, so while some animals may pick up numerous types of parasites, if they pick up the parasite that is "designed" for them, they can actually co-exist with it, asymptomatic, for a very long time.
2) Chemical de-wormers don't persist indefinitely in a chicken's system, and if used correctly, recommended withdrawal periods for eggs/meat will avoid indirect consumption of said chemicals. You also have to acknowledge the fact that if your chickens have worms, then their meat (depending on the species of worm and level of infestation) and eggs are likely to be contaminated by the parasites and may infect you/anyone else that comes in contact with the birds, areas the birds range, their meat, and/or their eggs.
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Your dog's feces should be routinely checked for worms as well, and treated if necessary (regardless of whether or not it eats chicken poop). It can pick them up the same way that the chickens can.