Agreed with Eckielady. I would tell neighbors that they are not to contact your dtr. Any communication needs to come directly to you. You are allowed to have chickens. As long as you are maintaining the zoning laws for your property, go about your business, and ignore the complaints. While chicken's egg songs can be loud, usually, they sing their song, and then they are done for the day. Got dogs in the neighborhood? Dogs yell for any and no reason all day long. And often, dogs are louder! Got lawn mowers, leaf blowers, any other power equipment? Cars with horns? Crows? I'm sure there are plenty of other noise makers in your neighborhood. While we all would like to dictate what goes on outside our windows, the reality of the situation is, that my rights end with my property line. And my neighbor's rights begin at my property line. I would not gift eggs to a complaining neighbor. If I gift eggs to anyone, it's to a friend, a relative, someone with a need, or to say thank you, or a barter. No gifts to reward crankiness.
You might consider planting some vegetation at your fence line. Vegetation is a great sound barrier.