She was, wasn’t she? I haven’t seen it in a long time, but I recall several scenes that implied that.
I also haven’t seen The Phantom Menace from beginning to end in a long time, but IIRC, Padme never flirts with Anakin, it’s Anakin who had a crush on Padme and does the awkward comments and unwanted catcalls. Which would fit in the typical the-male-character-has-the-iniciative narrative you see in lots of movies, including the pre-Disney Star Wars franchise.