As a professional dating coach I'd like to help you out here with how to text flirt:
Look, whether you like it or not, men have been chasing women for hundreds of thousands of years so don't expect it to change soon. In other words, women won't come to you when you do nothing. You need to take action to "get the girl", and that includes when you try and text flirt.
As some women have already said: they want to contact you first but often don't because they don't want to come across like they're desperate when they text flirt (or in any other situation for that matter).
And asking why you always have to contact her first is only showing that YOU are desperate. Because what's a girl supposed to answer: "ok OK my turn! But tomorrow it's your turn!" I don't think so.
So, you should be the one contacting her the most and taking action the most. Having said that, you should also look into how to text flirt
and create attraction. Who knows, maybe she doesn't respond that often or contact you first because you're doing something wrong.
And if you need help with attraction and how to text flirt, then do check out a ton of examples of how to text flirt (and some do's and don'ts) I've prepared for you on my blog!