So, for simplicity, Patryn's objection seems to hinge on whether a flurry of blows is performed as merely part of a full-attack action, or whether the full-attack action becomes a flurry of blows in its entireity.
It seems to me that there are plenty of examples of actions, as was pointed out by another poster, that may be performed only during a full-attack action, implying that they may be used synergistically. These include secondary natural attacks, two-weapon fighting, and (I claim) flurry of blows. And then there are examples of actions, like Whirlwind Attack, which specifically state that you must give up all your other attacks to do them (and would otherwise be combinable with things like two-weapon fighting).
Since nowhere does it state that flurry of blows cannot be used in the same full-attack action with other attacks, I don't see any problem. Flurry of blows seems to be a discrete action that provides extra attacks on top of the attacks you receive from your BAB, exactly as two-weapon fighting is. I find nothing that would make it impossible to combine them with secondary natural attacks (except as limbs become used to hold weapons), or with each other.
As far as this text is concerned:
SRD said:
When using flurry of blows, a monk may attack only with unarmed strikes or with special monk weapons (kama, nunchaku, quarterstaff, sai, shuriken, and siangham). She may attack with unarmed strikes and special monk weapons interchangeably as desired. When using weapons as part of a flurry of blows, a monk applies her Strength bonus (not Str bonus x 1-1/2 or x1/2) to her damage rolls for all successful attacks, whether she wields a weapon in one or both hands. The monk can’t use any weapon other than a special monk weapon as part of a flurry of blows.
It seems clear to me that this restriction is quite like the restriction on using light weapons during off-hand attacks to avoid large penalties, but with a stronger restriction. When making flurry of blows attacks, a monk weapon or unarmed strike must be used. When using an off-hand attack, it doesn't matter what weapon you use in your primary hand, so long as the off-hand is light. Likewise, it doesn't matter what weapon you use in your off-hand so long as your flurry attacks are made with the appropriate weapons. And likewise, it doesn't matter whether you claw-claw-bite so long as you apply the flurry restriction to the flurry attacks properly, and apply the flurry penalty to every other attack made that round, including the claw attacks.
Keep in mind, however, that the penalties from each source stack, and if you're hitting anything at all with your secondary attacks after stacking two-weapon fighting and flurry of blows penalties stacked on it, it's a miracle. I do suppose, however, that a strict reading might indicate that you apply the two-weapon fighting penalty only to attacks made by the primary hand, which would mean that the flurry attacks (since they're not necessarily made with a hand) and natural attacks (ditto), may not be affected.