They were Nieuport 28 types. Most were modified, typically with reduced span wings and fitted with cowlings canibalised from Thomas Morse Scouts. I'm not sure if there might have been a Garland Lincoln LF-1 in the Flynn version. The LF-1 was based on the general outline of the N28 and specially built for movie work.
A few ex-movie Nieuports survive, some brought back to a semblance of wartime standard. Several replicas of the type also exist, along with at least one Garland Lincoln LF-1.
Garland Lincoln LF-1
Welcome to the Forum. Hopefully someone will move your post upstairs where it will atract more attention.