Is it illegal to flip off a cop?
Precedent has been set down since the early 70s stating that profanity is in fact covered under the First Amendment.
Police try to cite people that use profanity with disorderly conduct charges. These charges are unconstitutional and most law enforcement agencies have training that specifies obscene gestures and language do not qualify as disorderly conduct.
Law enforcement agencies are regularly sued, and settle, when erroneous citations for disorderly conduct based on profane language and gestures are contested in court.