My biggest hang-up is continuing fun/flirty conversations with someone I've just met. I have no problem going up to a girl and opening her up and transitioning into something else (usually some kind of cold read), but if she isn't really into it I have trouble leading a conversation and keeping from going down the what do you do etc route. Any suggestions?
It's great that you've gotten past even that first step of approaching! That's more balls than most guys.
Anywho, you say if she isn't really into it...
Well, first let's check your outer game.
Do you have good hygiene? (brush teeth, ok-nice breath, smell good, clean, etc.)
Are you dressed nicely? (If you don't know... have you gotten compliments on your clothes? Or consult a men's fashion magazine such as GQ)
Hows your tonality? (does it vary, go up and down (in pitch) and keeps the girl interested? Ex. you can't always be excited, so are you happy, sad, tired, pumped?)
Facial expressions? Same as tonality
Body language? Are you open or closed? Are you standing up/sitting up straight or are you hunched over? Are you holding something in front of your chest? Or are your arms spread out in a warm manner?
If all those you checked as PERFECTO, then great! Moving on.
After you've fixed all outer game problems, you'll see HUGE improvements to your confidence. You'll look better, smell better, and most importantly, feel better.
If you just suck at flirting... Find a friend who will play improv games with you.
Or write down a list of things that'd make a girl your perfect girl. Memorize that list from A-Z and know it subconsciously. THEN, go out and make sure the girl fulfills each and every single thing on that list. If she doesn't, then she should be easier to talk to now that you know she's not the one and could be a new fuck buddy.