What you have to ask is if his film is a disney princess film? In my opinion it has to meet these there criteria; the princess must sing, they must marry or be born to royalty and they must be hand drawn. Does Flynn meet these? If he does, then yes, he is a prince, if not, he isn't.
Well ok I know what I am going to say isn’t in this spot but take Giselle from encantada for instance. She fell for a prince left him falls for a handsome attorney and her prince ended up with Nancy. Now I asked could Nancy be added and they said No so for Flynn Rider technically his not a prince but still he married Rapunzel. I wish he was added that dude is so cute for a cartoon character.