You seem to be arguing that you cannot use a two-handed reach weapon as part of a Flurry of Blows.
In actual fact the rule is that you cannot use any weapon other than Improved Unarmed Strike or one which has the "monk" special quality.
The original post, however had nothing to do with Flurry of Blows. It was specifically chasing the ability of a character to threaten both 5' and 10' from themselves while wielding a reach weapon if they have the Improved Unarmed Strike ability. The answer to this is yes, they do threaten, as Improved Unarmed Strike does not require hands to be free to make an attack.
As such, this allows the equipped character to make that Attack of Opportunity against the foe 10' away, and then with Combat Reflexes, they can also take an Attack of Opportunity with their Unarmed Strike. As the Attacks of Opportunity are standalone attacks and not part of a Flurry of Blows attack action, the character is entitled to use whichever weapon, or attack type, they feel is appropriate at the time (assuming the weapon can make the attack).
Flurry of Blows plays no part in determining the legality of the situation.
Hope this clears it up for you.