@VINT64— 
Properly, when used in reference to 
courting behavior, the verb “flirt” is 
intransitive, which is to say that it does not take a 
direct object.  Normally, the preposition for the indirect object is “with”, as in “He was flirting with another woman!”  This is somewhat misleading, as the other person may not be flirting in response, but that's how it goes. 
The 
transitive uses of “flirt” referring to 
striking, 
throwing, and 
blurting.  If someone flirts you, then you have been hit or propelled! 
There is an additional 
intransitive sense of “flirt”, referring to 
scoffing, 
sneering, 
jibing, or 
rejecting.
The term for one who flirts is not “flirter”, but just “flirt”, as in “My girlfriend is a flirt!”