My wife is first generation Greek-American, I live in a Greek neighborhood and have eaten Saganaki dozens of times.
Saganaki is NOT supposed to be like a dip. It is hard cheese, sometimes coated in flour and pan seared. It may be a little soft/stringy when eating it depending on the exact cheese used, but it is supposed to be cut and eaten in pieces.
None of the Greek restaurants around here serve it flaming either; it's unnecessary and really adds nothing to the dish aside from people wanting a spectacle with their dinner.