I would say an ESFP would be the flirtiest in the traditional sense. Se-doms probably intentionally flirt the most often.
SPs: Generally pretty good at flirting, I would say specifically that ISFPs would probably be the worst at it, but all in all I do not think any SPs would have a really difficult time of it. Able to observe someones behavior, and are generally able to run with whatever someone is saying in the moment to carry the conversation/flirting where they would like it to go. Generally do not get overly attached to the individuality of a person per-say, so are able to adjust and re-adjust to fit whoever they are with.
NFs- probably more avoid flirting until they are absolutely sure that there is an interest from the other person. Get emotionally involved with the idea of someone and then are hesitant to risk having their ideal version of that person challenged, so when they flirt it is more or less generally a long drawn out process of spilling their feeling for a person, which the other may or may not be aware existed.
SJs: This one is a bit hard. I would say that SJs would generally see the other person as a complimentary portion to themselves. They would go after the person who fits what they are looking for in a person, a partner, and/or an assistant. They would more likely want to shape the relationship, and would probably be the most likely to try to change parts of their partner that they do not personally like. Where as the NF would be disappointed when they found out something disagreeable about their partner and would probably try to regress away from the relationship, an SJ would be more likely to try to move forward and work with the punches.
NTs: Hmmm, this one is hard as well. Probably not the type most likely to flirt in the traditional sense. Possibly would become attached to how the person could stimulate them intellectually. Liable to fall in love with the personality and develop respect for a person before even realizing that they could have romantic feelings for them. Once the feelings do come out, they more than likely frighten the NT and since then NT is not completely used to dealing with strong emotions for sustained periods of time their romantic displays could possibly seem erratic to an outside observer.
These could all honestly be totally wrong, but took my best guess.