I haven't noticed any actual flirtation, but men definitely treat me with deference, and sometimes fall all over themselves to be chivalrous. We're talking mainly older men here (I'm 55). The women treat me like one of them, whether they know I'm trans or not (and there are an increasing number that DON'T know, for instance I've joined a church choir recently as guitarist, it's mostly women, and they all treat me as a woman, including one who shows signs of offering friendship). So I guess I'm passing pretty well these days. Been fulltime about 7 months.
In bed, I've had TWO men treat me as the woman I am! (!)