Flurry + 4 stunning strikes = 5 ki per round. And that is before the monk starts doing anything interesting.
As I said it is difficult to do that in combat, not impossible and what you describe is VERY difficult to do for 3 straight rounds.
First all 4 of those attacks have to hit or else you can't use the ki for Stunning Strike.
Second you need to be able to attack 4 enemies that are not already stunned - so hit one and if he fails his save you need to be able to get to another one (and hit him too) ...
Third up to three of those enemies need to be within 5 feet of each other because of the wording on FOB (i.e. "immediately after"). So you make an attack and stun a guy; if you want to use FOB and stun two more enemies, both of those enemies need to be within reach when you hit the first guy or you can't FOB on 2 more.
Finally you need to get 4 hits, in such specific conditions, for 3 straight rounds. While flights do commonly go longer than 3 rounds, they are often in mop up by the third round, and if your Monk was able to lay down 8 stunning strikes in the first two rounds, chances are it is over by round 3.
Bottom line, it will be extremely rare that you can do this, in this fashion. You either need to hit 4 different enemies with 3 in close proximity or you need to hit enemies and have them repeatedly make their saves, with each made save reducing the number of different enemies you need to attack by 1 and you need to do this three straight rounds. That is not easy to do.
Even without FOB, 3 attacks, each with stunning strike is not easy to do for 3 straight rounds, at least not in a manner that is tactically sound. You can do it easier if you are fighting an enemy with low AC an extremely high con save and legendaries, but in that case you are wasting ki on an enemy that isn't failing his save.
For the purpose of this discussion, I am obviously assuming that you are not wasting ki stunning an enemy that you already stunned this turn.