When a monk uses Flurry of Blows with nunchaku, and gets, say, two attacks, if she wants to use the nunchaku for both attacks she'd have to use two nunchakus, just as if the attack is with kamas she'd need two kamas. If the nunchaku were a double weapon, she'd only need one in this case, which seems to make sense for nunchaku (i.e., the same as a quarterstaff).
Or am I mistaken about FoB, and a monk needs just one special monk weapon to use it for all blows? The rules are not clear on this - it simply says the monk needs to use unarmed attack or special monk weapons. It doesn't say she needs two for two attacks with that weapon.
You can use the nunchaku (or a special monk weapon) for all flurry of blows attacks. Take your theory to its logical conclusion: if he didn't, how many weapons would the monk need at 20th level to flurry?
Also note that monks and TWF are a weird case compared to everyone else, one I won't get into here (but there are other threads for this).
I think that "monk weapons" mean that one can flurry with them, making all their flurry attacks with one weapon.
I don't know how flurrying with two weapons works. I suppose it would make a difference if one weapon was +1 holy and the other +1 flaming, at least it would to a troll.
Yes, weapon effects are all potentially different, so it does make a difference. So my assumption that you'd need two weapons to flurry with more than one is ungrounded - a monk holding a special monk weapon in one or both hands can choose to use that weapon for all flurry attacks, some of them or none of them. Presumably, if he (all my monks are male at the moment) had a kama in one hand and a nunchaku in the other, he could choose either of those or unarmed strike, for any of his attacks.
Thanks for the feedback!