You say the vet got her book out to check the correct dosage, and you are questioning it now on a forum rather than at the time with the vet?
As a vet myself, we don't prescribe medication for chickens as often as we do cats and dogs, and the medications are licensed for dogs and cats so the dosage on the bottle is for dogs and cats. We will usually have to look up the dosage for chickens to make sure it is correct and the most up to date evidence for that dose.
As chickens have a faster metabolism than dogs and cats, the dose is higher for chickens. The dose for dogs is 0.1mg/kg per day, so that is how the dog syringe is calibrated, so when chickens require a higher dose, it is usually a dose that is considerably more than their actual weight. 1mg/kg once a day is a very commonly used dose in chickens, so as this is 10 times the dog dose, your vet is absolutely correct to say to give 30kg dose for your 3kg chicken.
I hope your chicken feels better soon and you feel more confident to ask about the dose before leaving the practice if you are unsure about any medications in future.