The only flail mower I have used was for ag use and about 20 foot wide. This was a hitch mounted, 1000 pto driven unit. You are considering a 6' 3pt mounted version but the principles are the same. We would use them to cut the wheat stubble after harvest and some times to cut corn stalks etc. Can be used for grass but we never did. Except for the width of cut I never liked the thing. They are noiser than a rotary mower, need to be run at pto speed, where a rotary mower can be run at slower speed if desired. Hope you never hit a rock, metal, wood or even the ground because the racket it causes is so severe you would think something would break. When the knives hit something, they are thrown in every direction and essentially hit other knives, the metal center drum or anything else in the vicinty on the mower. No realistic way to ever sharpen all of those flail cutters. Don't plan on using it to cut brush, trees ect. In general, they also seem to be more prone to scalping the dirt on uneven ground.
The advantages of a flail mower I can think of is it's ability to be lighter in weight for the width of cut and they don't hang as far behind the tractor as a rotary mower. They would also be better for not clumping the grass as it is cut.