The flirting part and intention is where you need to tread delicately. It is "normal" for a person to question whether or not they want to hang on to a relationship that isn't working (at least at the moment)...
A lot of people are scared to be single... it seems as if this creates a lot more pain than if they had been single for the little while.
I know a lot of people flit from relationship to relationship (both girls and guys) never giving themselves a chance to figure things out or "mourn" a loss of a relationship, and this seems to create a lot of needless problems. But breaking it off, and getting a little time to be alone and think things through can help people improve themselves. The time people spend being single gives them time for reflection. Perhaps it's an effect of the "mourning" process... and people are mourning the death of a relationship; everyone does this differently and in their own way, but to me,
Logically, if you care about your reputation, it also cuts down on the amount of gossip; "Oh, he left me for another woman" or "he was trying to hook up with other girls" will be cut way down if you don't start dating someone else for a few weeks.
Remember that the grass is not always greener on the other side. However, if it's nothing but fighting, bickering, etc... heck, whatever the couple's problems are, even if it's something you've decided that you can't be around (without fighting over it), then it's time to leave. If it's a deal breaker, it's time to leave, but you need to make sure you're right first and that you give the relationship some respect and not be flirting.
I think that the more time you spend desiring someone else, the less focus you can give towards keeping/making your relationship healthy.
You need to be clear with BOTH your girlfriend (She needs to know (if it's not clear) that you're starting to question being in this relationship, and it's time to slow things down a bit, back off, and figure out what you both should do before you start to get too close to this other girl. Sometimes the current relationship needs to get back to the basics before you decide to break it off.) and this other girl (after you discuss it with your current S.O) know (without being cruel).
If you choose to pursue this with the new girl, 1) it might very well not work out; 2) be prepared for that 3) Give the current relationship a real effort before just leaving it; 4) "Prepare" her for the possibility of it not working; and if you decide to break up, break it off with class. Don't just "spring" it on her.
Don't just keep a "placeholder" until you find something better. If you want to try for something "better" for you, give it the attention it needs by being single for at least a few weeks; this may give you the time and focus a new relationship needs in order to develop.