Women are requesting authentic desire and attention and honesty. It requires conversation and getting to know the person between the ears and armpits and not the external view.
They do want male desire and they want authentic masculinity very badly. They honestly crave it, and they even take the leap when they have great fears.
There is an adage, men fear women laughing at them, and women fear men killing them. There are quite a few awesome guys out there, which may include you also (Don't know you so I can't judge), but there are a lot of bad guys out there. Remember a few guys can shade all of masculinity by their actions since their thirst and uncontrolled hunger and desire can cause damage that can arc for a long time with women.
So women don't desire the flirting of the past, they desire the real connection and engagement more then fifteen seconds. There time is valuable just like yours.
Remember this .... with raised standards come deeper connections and more powerful intimacy. Women understand how rare authentic male desire is, and they want to find it.
So be smart, find something out about the person and what they do, and then after one learns, then engage and you can use some of that flirting. Look at how women do it for men, since quite a few women make the choice of the male partner and not the other way around in traditional societys.