I'm surprised no one has said ESFP yet. Maybe they are the most flirtatious of the types rather than the best flirts? But for me personally, charm is the best way to lure me in and from my experience ESFP flirting has tons of that. I'm a sucker for SFP and to some extent NFP flirting
I would tend to think ESFP less inhibited than ESFJ, but ESFJ is going to have the edge because of Fe when they do chose to flirt, but ENFJ would be even better because they can use their N to guess what other people want to see/hear.
So best flirts overall for all types, in my opinion, in order:
ENFJ
ENFP
ESFJ
ESFP
ENTP
ESTP