
Well here ya go, and I have even numbered the steps for you:
NOTE: All mathematics used were based off of the 1.33/second swing time of a sword or axe. You could, however, replace this with 1.75/second swing time with a hammer, or refires/second with a bow, and get similiar results.
...First, we derive the damage over time for 5 seconds of normal attacks...
#1
5 / 1.33 = 3.759~ (swings in 5 seconds)
#2
3.759~ x 20* = 75.188 (damage output over 5 seconds)
...Now for damage over time for the 5 seconds under Flurry...
#3
5 / .8778 = 5.696~ (swings in 5 seconds)
#4
5.696~ x 15** = 85.441 (damage output over 5 seconds)
~ Indicates a long continuation of numbers.
* This number can be substituted for one on your choosing, i.e. try to pick one closest to your estimated damage per swing.
** This number is 75% of the first (or if you picked your own number, use 75% of it); in other words - you are dealing 25% less damage (obviously, as you are under Flurry).
Note: .8778 is 66% of 1.33; in other words - swing time under Flurry is .8778~ seconds per swing.
Now for a little old school algebra...and you thought what they taught you in school would never serve any real world use!

75.188
------
100
=
85.441
-----
x
x = 113.636~ (your damage output % under Flurry vs. normal)
So, after 5 seconds of Flurry, you have done approximately 113% damage over time as you would without.
Want more proof? Let's try using a 50 dmg baseline for avg. damage/swing. It comes down to this:
Normal: 3.759~ x 50 = 187.96~
Flurry: 5.696~ x 37.5 = 213.60~
187.96 damage vs. 213.60 damage over 5 secs. Need I go on?
Fine...

187.96
-------
100
=
213.60
------
x
x = 113.64~
Hmm...virtually identical increase in damage over time as the first set of numbers.
Basically, as you can see, there is an advantage to Flurry that many people do not realize. I too often seeing it being passed off as a crappy skill as compared to Frenzy, Tiger's Fury, etc., when it is obvious here that it not only provides increases in attack speed, increased adrenaline gain, AND increased damage over time, but it does so without any negative consequences (Frenzy - take double damage, Tiger's Fury - disables non attack skills for 5 seconds, etc.). However, it has a slightly shorter run-time than Frenzy (8 secs vs. 5) and Tiger's Fury (only if your Beast Mastery is equal or higher than 6, I believe).
Sure, you're still going to eke out a little more damage using Frenzy/Tigers Fury for the same 5 second duration. But maybe not safely. As said before you still get a 13% increase in damage over time versus normal, plus a 33% increase in adrenaline gain. What's not to like? Combine it all with a zealous haft/hilt, and you're golden.
Did I forget to mention that even just 5 seconds of Flurry is almost the perfect amount of time to charge up your adrenaline for spiking some of our favorite axe skills? And even if not, -zap-, right back into Flurry.

Do the pros outweigh the cons? To me they do. Then again, I'm not saying Flurry > Frenzy > Tiger's Fury, or anything to that nature. Just explaining the facts...
Go ahead and discuss, I know you want to. Though please keep it civilized and mature, as this is not a "skill 'a' is better than skill 'b'" topic.
Note: If I made any mathematical errors, please let me know, and I will correct.