I know the title is sort of an oxymoron-but this is the point!
We are living in the frum world, in Shidduchim and we remain tznius and proper-which is all great. There is no such thing as flirting (which in a way, makes the whole tznius issue aLOT easier) when it comes to Shidduchim for a number of reasons. The first that comes to mind is the following scenario:
you're at a wedding, looking your best from your makeup to your hair to your outfit, and there are LOADS of guys on the men side/hanging out in the hall. You had your eye on this cute guy at the chuppah and sure enough, as you come out of the bathroom from putting away the arches, THERE HE IS, leaning against the wall, laughing at something his friend said. You pass by, wink and give a half smirk. Later on, your friend asks you about a guy at the wedding: "do you know that guy?"
"Which one?" you ask?
"The one talking to Adina's cousin's husband" she says as she points to that cute guy you smiled at a few minutes before....
ok, so point #1 would be=most 'frum' men (and this is just my personal statistic) don't wear wedding rings. Sure, I know some guys who do, but when everyone is wearing dark suits at weddings, it's really hard to tell.
Another case in point, when you're dating a guy, until you are absolutely sure that you like him-you're so busy thinking and thinking ahead and future that you can't actually 'enjoy' his company together, so there's no time to really flirt.
Lastly, most girls in Shidduchim, after being 'in the system' for quite some time (well, enough to UNbrainwash them from sem and turn them back into NORMAL girls) will likely flirt with married guys and talk them up, to show how awesome they are and UNshy, in hopes that the married can find them someone.