I've had success using both Flannigan and Duckler correlations. The trick is understanding the assumptions that went into the development of the equations. I wrote a program for a client that required some degree of confidence in the effect of elevation changes and liquid hold-up on a flow stream. So I dug into the old literature and found the original papers on both correlations (before you ask, those papers are now in a box in another state and I'm not digging them back out) and reviewed their assumptions and their data. The assumptions worked for the program I was writing and their data looked applicable to the program so I used them. Other times they haven't fit with the goal of my calculation and I looked elsewhere.
Back in the dim dark slide-rule days, a lot of effort went into developing correlations that the average Engineer (who was no smarter, no more motivated, and no less lazy than today's crop) could successfully solve more times than not. Some of the correlations stood up to a wide range of problems and others were applied far outside their applicable range (e.g., Turner did his vertical flow analysis at over 1,200 psig and I see people today doing the "Turner Calculation" with 10 psig wellhead pressure), but all were more or less slide-rule friendly.
Flannigan is not evil, users of it just need to do their homework to determine where it has a chance of success. You have to dig pretty deep to find out why it has the parameters it has.
David