Do you have the Baytril label? There are different strengths, such as 100 mg per ml, and 22mg per ml. I am more familiar with the oral version 10%. So that will make a different in the amount given. However 3 ml would be a huge amount to give in a single injection.
Whenever my animals are given any medication at the vet, the exact amount administered is printed on the receipt. Check your receipt to see if your vet does the same.
FWIW: From Baytril website:
Ornamental birds im 20 mg/kg bw, once daily for five to ten consecutive days. In case of complicated infections, higher doses may be necessary.
If the vet was using the 2.5% solution, that would have been a 75 mg dose. It a 6 pound chicken, that is 27.5 mg/Kg or 33 mg/Kg in a 5 pound chicken.