Hi again. This entry intrigued me because I didn't know that the 1865 New York State census identified where soldiers were serving in the Civil War. So I learned something. Your ancestor appears to have been 40 in the 1865 census and 45 in the 1870 federal census. That is old enough that he would have been on the Class II list, married men over 35, had he registered for the draft, and not likely to be drafted. I see no relevant military records either, but if he was in the Army he wouldn't have been home to "lie", it would have been some one else. I don't think he would have needed to lie to avoid the draft either I just think it likely that it's just a mistake in the 1865 census which appears to be the only record of any kind that attributes this military service to him. They census personnel do make mistakes -- the field notes are transcribed onto the pages we see which does leave room for error. I was frustrated that I couldn't find a subject I was researching with a very common name, Gilbert Smith, in New York City -- he was in the furniture business. I finally realized that I had found him only his occupation was erroneously listed as "auctioneer". When I read down the page, I realized that the transcriber had just recopied the occupation of the head of household before him beside his name -- this was my man and there was no Gilbert Smith auctioneer.
Philip Flynn should have registered for the Draft and I don't see that he did that either, at least under first name Philip, but that doesn't matter, what you want to know is if he served in the Civil War. BTW are you sure the Philip Flynn of the 1865 census is your ancestor? That 1865 census does not show any daughters born in Philadelphia during the War. It shows all children born in Kings, meaning Brooklyn, Kings Co. NY But that could be another error. In these apartment buildings in New York City (actually, Brooklyn wasn't in NYC until 1898, but the situation was the same), you don't know who was giving the information, it could be a landord or landlady or another tenant, not necessarily family, not necessarily anyone who actually knew the information.
I really would not assume that anyone lied when I see mis-information in a census. Errors are just too common to attribute an intent on anyone's part to deceive unless you know you're looking for a scoundrel;-)