Give it down the right side (the chicken’s) in the back of the throat. See picture 4 in this article for where the syringe should be placed for giving small amounts of fluids:
https://unitedpeafowlassociation.org/articles/oral-medication-dosing-of-peafowl/
https://unitedpeafowlassociation.org/articles/oral-medication-dosing-of-peafowl/